Princeton Ch 9 - Electrostatics

Question 1

e =

Answer 1

Elementary charge. e = 1.6 *10^-19 C

Question 2

True or false. Total electric charge, like energy, is always conserved.

Answer 2

True. The total amount of charge before any process must always be equal to the total amount of charge afterward. If you scrub some e- off a cat you petted, then the cat loses X amount of e and thus charge, but you gain the same amount in magnitude.

Question 3

The electric force between two charged particles a distance r apart is described by the following equation.

Answer 3

F(E)= k* |q1q2| /r²

k = 9*10^9 Nm²/C²
q = [C]
r = [m]

Question 4

What does the proportionality constant in Columb’s law mean?

Answer 4

Its value depends on the material between the particles. But usually, the particles are separated by empty space, so we just use Coulomb’s constant:
k0 = 9*10^9 Nm²/C², unless we’re given another value (which would happen only if the charges were embedded in some insulating material that weakens the electric force).

Question 5

When it comes to two tiny charged, particles, which is stronger: gravitational or electric force.

Answer 5

F(E)= k* |q1q2| /r²
F(g) = GMm/r²

You’ll probably find that the electric force is much stronger than the gravitational force.

Question 6

Consider two plastic spheres (big and small) that are positively charged. If one sphere is fixed and the little sphere is free to move, describe the resulting motion of the little sphere released from rest.

Answer 6

The initial “a” of the little sphere released from rest is a = F(E)/m and the dir. is away from the big sphere. Bc the E force is 1/α to the square of the distance between charges, the repulsive force weakens, so it’s “a” decreases. The little sphere moves away with decreasing “a”. Since the “a” always points in the same dir., the speed of the little sphere is always increasing, though the rate of increase gets smaller.

Question 7

The principle of superposition for electric forces.

Answer 7

The net electric force on a charge (q) due to a collection of other charges (Q’s) is equal to the sum of the individual forces that each of the Q’s alone exerts on q.

Question 8

Describe electric force in in terms of an electric field.

Answer 8

The electric force on a second charge q is exerted by a field that the first change created.

Question 9

The charge(s) creating an electric field is/are called.

Answer 9

source charges.

Question 10

The convention is that we use a positive test charge q to determine the direction a point feels. Describe the direction of vectors in the presence of a negative and positive charge.

Answer 10

By convention, the electric field vectors always point away from positive source charges and toward negative ones.

Question 11

The closer we are to the source charge, the (weaker/stronger) the resulting electric force a test charge would feel.

Answer 11

The closer we are to the source charge, the stronger the resulting electric force a test charge would feel. Coulomb’s law is an inverse-square law.

Question 12

How many charges does it take to create an electric orce? An electric field?

Answer 12

Two charges to create an electric force. BUT, only one source charge to create an electric field.

Question 13

The formula for the electric field.

Answer 13

E(by Q) = k|Q|/r²; you just removed one of the charges from Coulomb’s law

r = just a position in space we want to know the electric field vector. 
"Q" = source charge. Can be 2Q, 3Q, etc.

Question 14

Define electric field.

Answer 14

The force per unit charge that a charge would experience at that point. This is a vector.

E(by Q) = F/q(test) = k|Q|/r² [N/C]

Question 15

What can the density of electric field lines tell us?

Answer 15

Where the field lines are cramped close together, the field is stronger; where the field lines are more spread out, the field is weaker.

Question 16

How does electric force related to electric field.

Answer 16

F(on q) = qE

Question 17

Whenever q is negative, the Force on q will always point in the (same/opposite) to the electric field.

Answer 17

Whenever q is negative, the Force on q will always point in the OPPOSITE to the electric field.

Question 18

True or false. A particle in an electric field has a constant acceleration.

Answer 18

The acceleration would change because the electric field is different in magnitude and direction in different places.

Question 19

True or false. The field will only do work (whether + or -) if there is a displacement in the direction of the electric field, or the opposite of the field.

Answer 19

A——->B; E field left

Question 20

The electric field vector at any point is (always/sometimes/never) tangent to the field line passing through that point and its direction is the same as that of the field line.

Answer 20

The electric field vector at any point is always tangent to the field line passing through that point and its direction is the same as that of the field line.

Question 21

Conductor.

Answer 21

A material is a conductor if it contains charges thata re free to roam throughout the material. Ex. metal. If a metal is placed in an electric field, these free charges will move in response to the field.

Question 22

An interesting property of conductors is the center. Elaborate on why.

Answer 22

Since e- repel each other, they’ll want to get away as far as possible from each other. As a result, excess charges move rapidly to the surface, Any net charge on a conductor is on its surface. Since there isn’t excess charge within the body, there isn’t an E field in the conductor. E = 0 on inside.

Question 23

Insulator.

Answer 23

A material that doesn’t have free charges. e- are tightly bound to their atoms and thus are not free to roam throughout the material.

Question 24

A neutral metal sphere encounters a positive charge Q without touching the metal sphere. What happens?

Answer 24

The(+) charge will attract free e- in the metal, leaving the far side of the sphere (+) charged. Since the neg charge is closer to Q than the (+) charge, they’ll be a net attract between Q and the sphere. Even though the sphere was neutral, the presence of Q will create a force of electrical attraction between them.

Question 25

A neutral insulated sphere encounters a positive charge Q without touching the metal sphere. What happens?

Answer 25

Although there aren’t any free e- that can move to the near side of the sphere, the atoms that make up the sphere will become polarized. That e- will feel a tug toward Q, causing atoms to develop a partial negative charge point toward Q.

Question 26

If an object moves “with nature” then the PE (increases/decreases). If an object moves “against nature” then the PE (increases/decrease)

Answer 26

If an object moves “with nature” then the PE decreases. If an object moves “against nature” then the PE increases.

Question 27

Electric potential ( for a point)

Answer 27

ϕ = kQ/r [J/C] –> note its just removal of r from the electric field equation.

Question 28

Is potential and electric force the same at every point around a circle?

Answer 28

Potential is because it’s a scalar. But, the electric force is a vector. So even though the magnitude might be the same, the direction is not. The sign of potential is important in determining the behavior of nearby charges if they are placed in a field.

Question 29

Change in electrical potential energy.

Answer 29

ΔPE = qΔϕ = qV; V is defined as the change in potential as is known as Voltage; q is the charge that moves between two points who potential difference is Δϕ(final) - Δϕ(initial).

Question 30

True or false. A charge experiences no change in PE when its initial and final positions are the same potential.

Answer 30

True. Like gravitational force, electric force is conservative.

Question 31

Positively charged particles naturally tend toward (lower/higher) potential and negatively charged particle tend toward (lower/higher) potential.

Answer 31

Positively charged particles naturally tend toward lower potential and negatively charged particle tend toward higher potential. All charged particles naturally move to positions of lower PE. See equation: ΔPE = qΔϕ

Question 32

Work done by an electric field.

Answer 32

W(done by Efield) = - ΔPE(electric)

Question 33

If the mechanical energy is conserved, KE+ PE is constant. If KE and PE are constant what must they equal and comment on the electric KE and PE.

Answer 33

ΔKE = - ΔPE

Question 34

Electron volt. eV

Answer 34

1eV = amount of energy for an e- to move from one position to another such than the change in E potential is +1V

1 eV = -1.610^-19J
1 e = -1.610^-19C

Question 35

Work done BY electric field versus AGAINST an electric field in terms of change in PE.

Answer 35

Work done against Efield = ΔPE = qΔϕ

Work done by Efield = -ΔPE

Question 36

An electric dipole consists of a pair of equal but opposite charges +Q and -Q, separated by a distance d. what is the electric potential midway between these sources charges? What is the E field?

Answer 36

The electric potential at the point P is zero. K(+Q)/0.5d + K(-Q)0.5d = 0.

The potential is 0, but the field is not. E(by Q) = k|Q|/r². The Efield would be 0, if the charges were the same sigh. Field is a vector. would cancel each other out.