Chapter 5: Electrostatics And Magnetism Flashcards
What happens when you shuffle your feet across the carpet? Use this an example to demonstrate what a ground is.
When you shuffle your feet across the carpet, negatively charged particles are transferred from the carpet to your feet, and these charges spread out over the total surface of your body. The shock that occurs when your hand gets close enough to a metal door knob allows that excess charge to jump from your fingers to the knob, which exes a ground - a means of returning charge to the Earth.
Is static charge buildup or static electricity more significant in dryer air or moist air?
Static charge buildup or static electricity is more significant in dryer error because lower humidity makes it easier for charge to become and remain separated.
What is the SI unit of charge? What are the units? What is the law of conservation of charge?
Compare and contrast insulators and conductors.
An insulator will not easily distribute a charge over its surface and will not transfer that charge to another neutral object very well, especially not to another insulator.
When a conductor is given a charge, the charges will distribute approximately evenly upon the surface of the conductor. Conductors are able to transfer and transport charges, and are often used in circuits or electrochemical cells.
Conductors are often conceptualized as nuclei surrounded by a sea of free electrons that are able to move rapidly throughout the material and are only loosely associated with their positive charges.
What materials make good insulators? What materials make good conductors?
Most nonmetals are insulators. Experimentally, insulator serve as dielectric materials in capacitors, as well as in isolating electrostatic experiments from the environment to prevent grounding.
Conductors are generally metals, although ionic solutions are also effective conductors.
MCAT concept check 5.1 page 169 Charges question 1
When placed 1 m apart from each other, which will experience a greater acceleration: one coulomb of electrons or one coulomb of protons?
The electrons will experience the greater acceleration because they are subject to the same force as the proton, but have a significantly smaller mass.
MCAT concept check 5.1 page 169 Charges question 2
MCAT concept check 5.1 page 169 Charges question 3
The charge will be negative one coulomb. Correction, 6x10^18 electrons per coulomb.
What is Coulombs law? What are the units?
When using Coulombs law, how do you obtain the direction of the force, in which way will the force point?
Proportionality example of positive and negative charges using Coulomb’s law page 170
Example of the relationship of electrostatic, force and gravitational force page 171
What is the ratio of the electrostatic force to the gravitational force between an electron and a proton?
Determine the magnitude and direction of the electric force of the proton on the electron in a hydrogen atom.
k=9x10^9 (N)(m^2)/(C^2)
dHydrogen = 1 angstrom
e= 1.6x10^-19 C
What is an electric field? What is a test charge? What is a source charge?
Every electric charge sets up a surrounding electric field, just like every mass creates a gravitational field. Electric fields make their presence known by exerting forces on other charges that move into the space of the field.
Whether the force exerted through the electric field is attractive or repulsive depends on whether the stationary test charge (q, the charge placed in the electric field) and the stationary source charge (Q, which actually creates the electric field) are opposite charges (attractive) or like charges (repulsive).
How can you calculate the magnitude of an electric field?
Electric fields are produced by source charges (Q). When a test charge (q) is placed in an electric field (E), how can you calculate the electrostatic force (Fe) felt by the test charge q?
By convention, what is the direction of the electric field vector?
By convention, the direction of the electric field vector is given as the direction that a positive test charge (q)
would move in the presence of the source charge (Q).
If the source charges positive, then the test charge would experience a repulsive force, and would accelerate away from the positive source charge.
On the other hand, if the source charges negative, then the test charge would experience an attractive force, and would accelerate toward the negative source charge.
Therefore, positive charges of electric field vectors that radiate outward (that is, point away) from the charge, or is negative charges have electric field vectors that radiate inward (point toward) the charge.
What are field lines?
Field lines are imaginary lines that represent how a positive test charge would move in the presence of the source charge. The field lines are drawn in the direction of the actual electric field vectors, and also indicate the relative strength of the electric field at a given point in the space of the field.
The lines are closer together near the source charge and spread out at distance as farther from the charge. Where the field lines are closer together, the field is stronger. Where the lines are farther apart, the field is weaker.
Because electric field and electrostatic forces are both vector quantities, it is important to remember the conventions for their direction. What are the conventions for their direction?
If the test charge within a field is positive, then the force will be in the same direction as the electric field vector of the source charge.
If the test charge is negative, then the force will be in the direction opposite to the field vector of the source charge.
MCAT concept check Coulombs Law page 173 question 1
The electric field would be zero because the two charges are the same. In this case, the fields exerted by each charge at the midpoint will cancel out and there will be no electric field.
MCAT concept check Coulombs Law page 173 question 2
For a pair of charges, a negative electrostatic force points from one charge to the other (attractive), while a positive electrostatic force points from one charge away from the other (repulsive).
Don’t overthink this. This is only a matter of convention and the direction refers to the net force when a positive test charge is placed around the electrostatic force.
MCAT concept check Coulombs Law page 173 question 3
MCAT concept check Coulombs Law page 173 question 4
Electrostatic force is directly related to each charge and related to the distance by an inverse square relationship.
Electric field is unrelated to test charge, but is still related to distance by an inverse square relationship.
Note that it is the source charge that creates the electric field, not the test charge, so we cannot use the equation E=Fe/q.
What is electric potential energy?
Similar to gravitational potential energy, this is a form of potential energy that is dependent on the relative position of one charge with respect to another charge or to a collection of charges.
Electric potential energy is the work necessary to move a test charge from infinity to a point in space in an electric field surrounding a source charge.
Given by the equation:
What happens to electrical potential energy of a system when two like charges move towards each other? When they move away from each other?
What happens to electrical potential energy of system when to unlike charges move towards each other? When they move away from each other?
Electric potential energy example page 175
This is a simple plug and play question using the equation for electric potential energy.
Be sure to convert nanometers to meters (1 m = 10^9 nm)
Getting better at the math!
Consider a stationary negative source charge a positive test charge that can be moved. What kind of force will they feel between them? Are they more stable or more unstable the closer they get to each other? That being said, what will the sign of the potential energy be?
Because these two charges are unlike, they will exert attractive forces between them. The closer they are to each other, the more stable they will be. Opposite charges will have a negative potential energy, and this energy will become increasingly negative as the charges are brought closer and closer together. This decrease in energy represents an increase in stability.
Consider a stationary positive source charge and a positive test charge that can be moved. What kind of force will they feel between them? Are they more stable or more unstable the closer they get to each other? That being said, what will the sign of the potential energy be?
MCAT concept check Electric potential energy page 176 question one
MCAT concept check Electric potential energy page 176 question 2
MCAT concept check Electric potential energy page 176 question 3
MCAT concept check Electric potential energy page 176 question 4
Equations for:
Magnitude of electrostatic force Magnitude of electric field
Electric potential energy
Electric potential
What is the definition of electric potential? What are the units of electric potential? Is electric potential a vector or scalar quantity?
Electric potential is defined as the ratio of the magnitude of a charges electric potential to the magnitude of the charge itself.
Electric potential is a scalar quantity, and it signed is determined by the sign of the source charge Q.
What is voltage?
Voltage is the potential difference between electric potentials.
Because electric potential is inversely proportional to the distance from the source charge, a potential difference will exist between two points that are at different distances from the source charge.
If Va and Vb are the Electric potentials at points a and b respectively, then the potential difference between them, known as voltage, is Vb-Va.
Charges, if allowed will move spontaneously in whatever direction results it decrease an electric potential energy.
For a positive test charge, this means moving from a position of higher electric potential to a position of lower electric potential. The voltage,
deltaV=Vb-Va=Wab/q, is negative in this case; because q is positive (for a positive test charge), thus, Wab must be negative, which represents a decrease in electric potential energy.
Now consider a negative test charge. A negative test charge will spontaneously move from a position of lower Electric potential to a position of higher electric potential. The voltage,
deltaV=Vb-Va=Wab/q, is positive in this case; because q is negative (for a negative test charge), Wab must also be negative, which again represents a decrease in electric potential energy.
What is the take away from the statement?
The Takeaway: positive charges will spontaneously move in the direction that decreases their electric potential energy (negative voltage), negative charges will spontaneously move in the direction that increases their electric potential (positive voltage), YET IN BOTH CASES, THE ELECTRIC POTENTIAL ENERGY IS DECREASING.
Four equations:
Coulombs Law (magnitude of the electrostatic force) (Fe)
Magnitude of electric field (E)
Electric potential energy (U)
Electric potential (V)
There is a box with four quadrants that helps remember these. Do it.
These are essential equations for test day. Know how they relate to each other and when to use them. By memorizing Coulomb’s law, you could be able to re-create the table through mathematical manipulation:
From left to right, multiplied by r.
From top to bottom, divide by q.
MCAT concept check Electric potential page 178 5.4 question 1
What is the difference between electric potential and voltage?
Electric potential is the ratio of a charges electric potential energy to the magnitude of the charge itself.
Voltage, or potential difference, is a measure of the change in electrical potential between two points, would provide an indication of the tendency towards movement in one direction or the other.
MCAT concept check Electric potential page 178 5.4 question 2
How will a charge that is placed at a point of zero electric potential move relative to a source charge?
A charge will move in such a way to minimize its potential energy. Placing a charge at a point of zero electric potential does not indicate that there is zero potential difference, so the charge may or may not move. If the charge moves, it may move toward or away from the source charge, depending on the sign of the source charge and test charge.
MCAT concept check Electric potential page 178 5.4 question 3
True or False:
The unit of electric potential energy and electric potential are different.
True. The units for electric potential energy the Joule ((Kg)m^2/s^2).
Electric potential and potential difference (voltage) are measured in volts (V=J/C)
How many electrons are in one Coulomb?
Chemistry throwback because why not.
What is the Henderson Hasselbalch equation? What does it determine for us?
Bonus. When does pH equal pKa?
pH equals pKa when the concentrations of the conjugate base and weak acid are equal (as log(1)=0).
What is electrical potential energy (U)?
Electrical potential energy of a charge Q at point and space is the amount of work required to move it from infinity to that point.
What is Electric potential?
Electric potential is the amount of work required to move a positive test charge q from Infiniti to a particular point divided by the test charge.
Remember this is voltage. Voltage is Joules per coulomb. We can extrapolate that it is energy per charge.
What is potential difference (Voltage)?
What is an equipotential line?
An echo potential line is a line on which the potential and every point is the same. That is, the potential difference between any two points on an equipotential line is zero.
Equipotential line example page 179
Work depends only on the potential difference and not on the path, as electrostatic force is a conservative force, so any of the paths shown would require the same amount of work and moving the electron from a to b. Remember that in conservative forces, the path taken is irrelevant, only the displacement matters for work as the equation for work is force times displacement times the cosine of the angle.
This is an important part to understand: because the test charges negative, the electric potential is higher at point B then point a. This should make sense because the electron will have to gain energy to be moved farther away from positive source charge (proton). Use the relationship of energy levels of electron orbitals to associate with higher or lower potential energy.
What is an electric dipole? What are some examples of electric dipoles?
Electric dipole results from two equal and opposite charges being separated, a small distance d from each other.
Dipoles can be transient (as in the case of the moment to moment changes in electron distribution that create London dispersion forces) or permanent (as in the case of the molecular dipole of water or the carbonyl function group).
Describe this picture:
Draw a generic electric dipole and derive the equation for a dipole moment. Page 180
There’s a lot here to digest.
Recall V=kq/r.
There are two assumptions made, and those are:
1) For points and space relatively distant from the dipole moment (compared to d), the product of r1 and r2 is approximately equal to the square of r.
2) And r1-r2 is approximately equal to dcostheta.
Two facts also to consider:
1) for a collection of charges, the total electric potential at a point in space is the scalar sum of the electric potential due to each charge.
2) the product of charge and separation distance is defined as the dipole moment (p=qd)
We combine the diagram for a general dipole, the two assumptions, the definition of a dipole moment, and total electric potential at a point in space is the scalar sum of the electric potential due to each charge, and we come up with the following image:
What is a dipole moment (p) defined as? What are the SI units of the dipole moment? What is the equation for the dipole moment? Is the dipole moment a scalar or vector or quantity?
How do physicist defined the dipole moment vector? How does this differ from the way a chemist by convention would define the dipole moment vector?
Physicist defined the vector along the line connecting the charges (the dipole axis) with the vector pointing FROM the negative charge TOWARD a positive charge.
Chemists usually have p point FROM the positive charge TOWARD the negative charge.
Recall that in Chemistry notation, a cross hatch is drawn at the tail end of the dimple vector to indicate that the tail end is the positive charge.
Dipole moment, example page 181
Don’t overthink this one. It is a simple plug and play with unit conversions.
This question states that the dipole moment is along the access of the dipole, meaning that theta equals zero, and cos(0)=1. This reduces the equation to:
V=kp/r^2
Then proper algebra. We did get confused about the dimensional analysis of this and needed to just accept that I am solving for electric potential which is voltage with units of volts (J/s).
What is the perpendicular bisector of the dipole? Why is an important echo potential line to be aware of?
One very important equipotential line to be aware of is the plane that lies halfway between +q and -q, this plane is called the perpendicular bisector of the dipole. Because the angle between this plane and the dipole axis is 90°, and cos(90°) is zero, the electric potential at any point along this plane is zero, given
V=(kqd/r^2)costheta=(kp/d)costheta
However, there still will be an electric field on the perpendicular bisector of the dipole, which can be approximated with an equation.
At a point on the perpendicular bisector of an electric dipole, which way will the the electric field vectors will point?
At a point on the perpendicular bisector of an electric dipole, the electric field vectors will point directly away from the negative charge and towards the positive charge; essentially, along the line connecting the two charges, due to the symmetry of the situation where the contributions from the positive and negative charges cancel out in the perpendicular direction.
MCAT concept check equipotential lines and electric dipoles page 183 question 1
Define equipotential lines.
Define electric dipole.
Equipotential lines are the sets of points within a space at which the potential difference between any two points is zero. We can visualize this as concentric spheres surrounding a source charge (like a hydrogen atom).
An electric dipole is the separation of charge within a molecule, such that there is a permanent or temporary region of equal and opposite charges at a particular distance. Water has a permanent dipole, nonpolar molecules have London dispersion forces as their primary dipole.
MCAT concept check equipotential lines and electric dipoles page 183 question 2
What is the voltage between two points on an equipotential line?
Will this voltage cause a charge to move along the line?
There is no voltage between two points on an equipotential line, so there will be no acceleration along the line.
However, there is a potential difference between different sets of equipotential lines, which can cause particles to move and accelerate.
MCAT concept check equipotential lines and electric dipoles page 183 question 3
Why is the electric potential at points along the perpendicular bisector of a dipole zero?
Recall that Electric potential energy is the work necessary to move a test charge from infinity to a point in space in an electric field surrounding a source charge. Given that Electric potential energy is work, it is a dot product which uses cosine (remember dot com, dot cos mnemonic) and the cosine of 90° is zero.
Theta in these generic dipole examples is in reference to the angle between the plane and the dipole axis.
MCAT concept check equipotential lines and electric dipoles page 183 question 4
What is the behavior of an electric dipole when exposed to an external electric field?
A dipole will rotate with an external electric field, such that it’s dipole moment aligns with the field.
How is the dipole a classic example of a set up upon which torques can act?
In the absence of an electric field, the dipole axis can assume any random orientation. However, when the electric dipole is placed in a uniform electric field, each of the equal and opposite charges of the dipole will experience a force exerted on it by the field. Because the charges are equal and opposite, the forces acting on the charges will also be equal in magnitude and opposite directions, resulting in a situation of translational equilibrium.
What is the equation for the magnitude of the electric dipole moment? What are the units of the electric dipole moment?
What is the equation for the net torque on a dipole in an electric field?
Which way will the electric dipole shown in the image rotate due to the torque produced by an external electric field?
Talk a little bit about the equation for network about the center of a dipole axis.
The dipole moment will rotate clockwise. Here’s why:
Do a force analysis on this. Using this coordinate system, the electric field is pointing right and the dipole is perpendicular to it. Think of torques and lever arms, they are a cross product of force applied and the lever arm multiplied by sin of the angle between the force applied and the lever arm.
Is the electric potential at some point P near a dipole a dot product or cross product? (do we use cosine or sine?)
What is the electric potential on the perpendicular bisector of a dipole?
Is net net force felt by a dipole a dot product or cross product (do we use cosine or sine)?
What is a magnetic field?
Any moving charge creates a magnetic field.
Magnetic fields may be set up by the movement of individual charges, such as an electron moving through space; by the mass movement of charge in the form of a current through a conductive material, such as copper wire; or by permanent magnets
What are the SI units for a magnetic field? What is a commonly used unit for small magnetic fields?
What is diamagnetic, paramagnetic, ferromagnetic?
Diamagnetic materials are made of atoms with no unpaired electrons and that have no magnetic field. These materials are slightly repelled by a magnet, and so can be called weekly anti-magnetic. Wood, plastics, water, glass, skin.
Paramagnetic materials will become weekly magnetized in the presence of an external magnetic field, aligning the magnetic dipoles of the material with the external field. Upon removal of the external field, the thermal energy of the individual atoms will cause the individual magnetic dipoles to re-orient randomly so that the material itself creates no magnetic field. Aluminum, copper, and gold.
Ferromagnetic materials will become strongly magnetized when exposed to a magnetic field or under certain temperatures.
Compare and contrast, paramagnetic materials and ferromagnetic materials.
The atoms of both paramagnetic and ferromagnetic materials have unpaired electrons, so these atoms do not have a net magnetic dipole moment.
Ferromagnetic materials will become strongly magnetized when exposed to a magnetic field (iron, nickel, cobalt) paramagnetic materials will become weekly magnetized in the presence of an external magnetic field (aluminum, copper, gold).
How do we calculate the magnitude of the magnetic field produced by a current carrying wire?
What is the magnitude of the magnetic field at the center of a circular loop for a circular loop of current carrying wire with radius r?
What’s the equation for magnitude of an electric field, created by a length of wire or a loop of wire? What accounts for the difference?
The equations are similar with two differences. The obvious difference being that the equation for the magnetic field, at the center of the circular loop of wire does not include the constant pi.
The less obvious difference is that the first expression gives the magnitude of the magnetic field at any perpendicular distance, r, from the current carrying wire, while the second expression gives the magnitude of the magnetic field only at the center of the circular loop of current carrying wire with radius r.
How can we use the right hand rule to determine the direction of the field vectors in a current carrying wire?
Straight wires create magnetic fields in the shape of concentric rings, a circular loop of current carrying wire produces a magnetic field at the center of the circular loop of wire.
Put your thumb in the direction of the current and wrap your fingers around the current carrying wire. Your fingers then mimic the circular field lines, curling around the wire.
Example of magnitude in a current carrying wire and direction of magnetic fields produced page 186.
Answer in Tesla and gauss.
What is the Lorentz force?
The Lorentz force is the sum of electrostatic and magnetic forces.
Charges often have both electrostatic and magnetic forces acting on them at the same time. The sum of these electrostatic and magnetic forces is known as the Lorentz force.
We reviewed ways in which magnetic fields can be created. Do magnetic fields exert forces on stationary charges?
Magnetic field exert forces only on other moving charges.
Charges do not “sense“ their own fields, they only sense the field established by some external charge or collection of charges.
Therefore, in the studies of magnetic forces on moving charges in on current carrying wires, we will assume the presence of a fixed and uniform, external magnetic field.
What is the equation for magnetic force when a charge moves in a magnetic field?
What is sin(0°)?
What is sin(180°)?
Sin(90°)?
0
0
1
Given the equation of a magnetic force when a charge moves in a magnetic field, magnetic force is a function of the sign of the angle. What does this mean?
The magnetic force is a function of the sign of the angle, which means that the charge must have a perpendicular component of velocity in order to experience a magnetic force. If the charge is moving parallel, or anti-parallel to the magnetic field vector, it will experience no magnetic force
A moving charged particle will experience 100% of the total potential magnetic force when moving perpendicular to the magnetic field. When it is moving 45° from the magnetic field, it will experience 70% of the total potential magnetic force. And so on.
What is the right hand rule to determine the direction of the magnetic force on a moving charge?
Position your right thumb in the direction of the velocity vector.
Put your fingers in the direction of the magnetic field lines.
Your palm will point in the direction of the force factor for a positive charge, whereas the back of your hand will point the direction of the force factor for a negative charge.
There is a pneumonic kind of device for the right hand rule for magnetic force. What is it?
Example of moving charge through a uniform magnetic field page 188.
We need to use the right hand rule here. Thumb points in direction of velocity, fingers point in direction of magnetic field. Protons are positively charged, thus the direction of palm faces the direction of the magnetic force on the proton (if it were a negative charge, back of hand faces direction of magnetic force).
When the question asked us to describe the resulting motion, we need to realize that the centripetal force is equal to the magnetic force. Set them equal and solve for r, which is the radius of the motion of the proton in the magnetic field.
What is the equation for a current carrying wire placed in a magnetic field experiencing a magnetic force?
This should make intuitive sense. The force felt is the function of the current flowing in the wire, the length of the wire, the magnitude of the magnetic field, and the sine of the angle between L and B.
We can use the right hand rule here to determine the direction of the magnitude of the force created by an external magnetic field. Thumb points and direction of current, fingers point and direction of magnetic field, vector, palm faces direction of force vector for positive charges, back a hand face direction of force vector for negative charges.
Example of force created by an external magnetic field on a current carrying wire placed in a magnetic field page 189
What are the requirements to have a non zero electric field, a non zero magnetic field, a non zero magnetic force?
To create an electric field, one needs a charge.
To create a magnetic field, one needs a charge that must also be moving.
To have a non zero magnetic force, the moving charge cannot be parallel to the magnetic field (put another way, it must have a perpendicular velocity component in order to satisfy Fb=qvsintheta) To put another another way: one needs an external electric field, acting on a charge, moving any direction except parallel or anti-parallel to the external field.
MCAT concept check 5.6 magnetism page 190 question two
This is a great question to exercise constants, variables, and proportionality.
We need to recall the magnetic field equations for conducting wires and loops of conducting wires.
We see that current, the current constant (duh), and r are all constant in the question.
MCAT concept check 5.6 magnetism page 190 question 3
Right hand rule exercise for direction of magnetic force.
First of all, we need a moving charged particle to experience a magnetic force. Second of all the moving charged particle will not experience a magnetic force if the direction of the charge particle is parallel or anti-parallel to the magnetic field (must have a perpendicular component in order to experience the magnetic force as Fb=qvsintheta and sintheta(180° and 0° is zero)
The right hand rule for magnetic force vectors is:
Thumb points in the direction of velocity vector, fingers point in direction of magnetic field vector, magnetic force will be the direction your palm is facing for a positively charged particle, and will be the direction of the back of your hand for a negatively charged particle.
MCAT mastery electrostatics and magnetism page 162 questions 1,2, and 3.
Question one: Newton‘s third law tells us that if R exert force on S, then S exerts a force with equal magnitude, but opposite direction back on R.
Question two: the force is inversely proportional to r squared. It’s an important skill to recognize proportionality on the MCAT. Image shows how to reason through that using algebra.
Question three: an electric fields direction at a given point is defined as the direction of the force that would be exerted on a positive test charge in that position. Because electrons are negatively charged particles, they will therefore feel a force in the opposite direction of the electric fields vector. In this case, because the force points to the left, towards R, an electron will feel a force pointing to the right (towards S) if E is in the direction of F.
MCAT mastery electrostatics and magnetism page 162 question 4
Remember that the magnitude of the electric field is inversely proportional to the square of the distance.
It is important to be able to set this up and solve the proportionality problem algebraically.
MCAT mastery electrostatics and magnetism page 162 question 5
MCAT mastery electrostatics and magnetism page 162 question 6
This seems like a question that we can expect to see on the MCAT.
Change in potential energy and change in potential are related by work.
MCAT mastery electrostatics and magnetism page 162 question 7
MCAT mastery electrostatics and magnetism page 162 question 8
Draw an image of the current carrying wires. Use the right hand rule (thumb pointing in direction of current, fingers coil in direction of magnetic field). Doing this allows us to determine that the magnetic fields will be additive as they are going in the same direction at point P.
Using the equation of magnetic field generated by moving current through wires, we see that the magnetic field is directly proportional to the current. If we double the current, we double the magnetic field.
MCAT mastery electrostatics and magnetism page 163 question 9
We know that the electric potential at the perpendicular bisector of the dipole axis is zero. We also know that the electric potential is zero and infinity.
Electric die cosine
MCAT mastery electrostatics and magnetism page 163 question 10
MCAT mastery electrostatics and magnetism page 163 question 11
MCAT mastery electrostatics and magnetism page 164 question 12
Voltage is equal to the quotient of the amount of work done divided by the charge of the particle on which the work is done.
Interesting, this gives us units of Volt Coulombs, which is a Joule, a unit of energy. Remember this.
MCAT mastery electrostatics and magnetism page 163 question 13
MCAT mastery electrostatics and magnetism page 163 question 14
Opposite charges attract. When I was opposite charged species are moved apart, their potential energy will increase because they would like to move back to a closer distance.
Then using the formula for electric potential energy (U=kQq/r) We know that U is proportional to 1/r, meaning that if r is changed by a factor of two, then U will also change by a factor of two (not a factor or four).
Think about it like this. An electron needs more energy to get farther away from the proton, therefore it has a higher potential energy. We can extrapolate that the electric potential energy would increase. We do, however, still need to know the equation for electric potential energy and its relationship to r.
Equations on whiteboard from chapter 5, electrostatics and magnetism
