Electricity

Question 1

Electric Charge - Properties and understanding

Answer 1

The SI unit of electric charge is the coulomb, which is given the symbol C. Electric charge can be positive, negative or zero. An object carrying positive electric charge is said to be positively charged, an object carrying negative electric charge is said to be negatively
charged, and an object carrying zero or no electric charge is said to be neutral.
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Electric charge is a fundamental or intrinsic property of electrons and protons. The electric charge of a proton is e = 1.602 × 10^−19 C and the electric charge of an electron is −e. The neutron is neutral.
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That charge only ever comes in discrete packets of a fixed size e is summarised by saying that the charge is quantised and that the quantum of charge is e. The quantity e is a fundamental constant of nature and is often called the elementary charge. The net charge or total charge of any object is just the sum of all of the charges of all of the protons and electrons which make up that object.

Question 2

What does it mean when an electric charge is conserved and what is the continuity of charge?

Answer 2

Electric charge is conserved, which means that the total amount of charge in an isolated system (or in the entire universe) is fixed and cannot change. By saying that charge is conserved in an isolated system, we are saying that overall for that system, charge cannot be created nor destroyed and the total amount never changes.

a continuity of charge in our universe. Roughly speaking, by the phrase ‘continuity of charge’ we mean that charge cannot disappear from one place and suddenly reappear at some other distant place, rather it must flow continuously from one place to another. Therefore it also must satisfy the law of continuity of charge, which more precisely states that the flow of charge into any small region of space must be equal to the accumulation of charge in that small region plus the flow of charge leaving that small region.

Question 3

What is global conservation law and local conservation law?

Answer 3

a global conservation law, a law which says that globally (or ‘on the whole’ or ‘overall’) in an isolated system a specific quantity cannot change. Charge continuity, in contrast, is an example of what physicists call a local conservation law, a law which says that locally (or in ‘tiny regions of space’) a quantity flowing into any small region of space must be equal to the accumulation of that quantity in that region plus the flow of the quantity leaving that region. Local conservation laws are said to be stronger than global conservation = laws because the observation that a quantity is locally conserved means that it must be globally conserved, but not the other way around

Question 4

What is Coulombs law and its formula?

Answer 4

F = (1/(4pie0)) * (|q1q2|/r^2), where e0 = 8.85 × 10−12 C2 N^−1 m^−2 is a constant of nature called the permittivity of the vacuum or the permittivity of free space or the permittivity constant.

Where is can also be F = k (|q1q2|/r^2), where k = 8.99 × 10^9 ≈ 9.0 × 10^9 N m^2 C^−2 (answer for the solved part)

Question 5

What is the electric field and its formula?

Answer 5

If the charge q is positive, then the direction of this force is in the direction of the electric field at the point where the object is placed. If the charge q is negative, then the direction of the force is in the opposite direction of the electric field at the point where the object is placed. The electric field strength, E, also known as the magnitude of the electric field, has units of newton’s per coulomb (N C−1).

Question 6

What is the electric potential?

Answer 6

When a charged particle of charge q moves (or is moved) from one point in an electric field to another, its electrical potential energy U changes (just like the gravitational potential energy of a mass moving in a gravitational field). The change of the electrical potential energy ∆U of the charged particle when it is moved between these points is given by the expression ∆U = V q where V is the potential difference or voltage between the two points. Potential difference is measured in SI units of volts (V), or equivalently in joules per coulomb (J C−1).

Question 7

What is an electronvolt?

Answer 7

1.000 eV = 1.602 × 10^−19 J Definition of the electronvolt

Question 8

What is the relationship between the magnetic and electric flux and its formula

Answer 8

The amount of magnetic flux |ΦB| through an area A⊥ which is everywhere perpendicular to a constant magnetic field of magnetic field strength B is given by |ΦB| = BA⊥ .

Question 9

What stuff is everything made from? and what holds the stuff together?

Answer 9

Particles and fields

Question 10

What are the 4 forces in nature?

Answer 10

1. Electromagnetic. This interaction holds electrons in orbit around the nucleus of an atom, holds magnets to your fridge, powers your phone and stops you falling through the floor.
2. Gravitation. This interaction holds the earth in orbit around the sun and you to the floor.
3. Strong nuclear. This interaction holds quarks together to form neutrons and protons, and holds neutrons and protons together inside the nucleus of an atom.
4. ## Weak nuclear. This interaction is responsible for radioactivity and the nuclear reactions within the sun.The electromagnetic field is generated by electric charge. This field can place forces on any particle that carries an electric charge.
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   The gravitational field is generated by gravitational charge, which is better known as mass. This field can place forces on any particles which also have mass
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   The strong charge is known as colour 4 and any particle carrying colour charge can participate in strong interactions.
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   The charge responsible for the weak interaction is simply known as weak charge. Any particle carrying weak charge can participate in weak interactions.
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   Electric charge comes in two basic kinds, which we call positive and negative. This fact manifests itself as electric charges being able to attract or repel one another

Question 11

What are Maxwells equations?

Answer 11

∇ · B = 0 and ∇ · E =ρ/e0, where p is the electric charge density and where B and E are vectors

Question 12

What is the Lorents force law?

Answer 12

F= q(E+ v × B ), where F, E, v and B are all vectors

Question 13

Vectors

Answer 13

LOOK AT NOTES BUT YOU HAVE:
- Vector components
- Magnitude of a vector
- Vector equality
- Vector addtion and subtraction
- Scalar multiplication
- Dot product (including propertities)
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- Scalar fields: A scalar field in a region of space is the assignment of a number (i.e. a scalar) to each point in that space at each instant.
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- Vector Fields: A vector field in a region of space is the assignment of a vector to each point in that space at each instant.

Question 14

What are fields/flux lines?

Answer 14

Another method of visualising vector fields is not to draw arrows, but rather to draw curved lines. These lines are called field lines or flux lines and they are carefully constructed so that at each point in space they are tangent to the vector at that point.

Question 15

What is the electric field and its formula?

Answer 15

The electric field is a vector field, and so in defining it we need to associate a vector with each point in space and time. The formula is given as E = F/q0, where E and F are vectors and since the units of force are newtons (N) and the units of charge is coulombs (C), the units of the electric field is newtons per coulomb (N C−1).

Question 16

What is the formula for the force on a charge in an electric field?

Answer 16

It follows immediately from the definition that if we know the value of the electric field E at a given point P, then we can determine the total electric force F that would act on a charge q if it were to be placed at P, it is: F = qE, where F and E are vectors

Question 17

What is the formula for the electric field of a point charge?

Answer 17

There are two depending if you are given a vector or not:

E = (1/(4pie0)) * (q/r^2) * r(vector)

E = (1/(4pie0)) * (q/r^2)

Question 18

Define source and sink in relation to electric fields

Answer 18

It is for this reason that positive charges are called sources of electric field lines and negative charges are called sinks of electric field lines.

Due to this comparison, sometimes the sources and sinks of electric field lines are called electric monopoles.

Question 19

Define Charge Distributions

Answer 19

Arrangements of electrical charge spread throughout space

Question 20

The Principle of Superposition (for electricity)

Answer 20

The principle of superposition states that if you are given a distribution of point charges, the total electric force acting on any one of the particles in the distribution is the vector sum of all the individual forces – determined by Coulombs’s law – placed on that particle by all other point charges in that distribution.

Question 21

What are the rules for drawing electric field line diagrams?

Answer 21

1. Field lines are always tangent to E at each point, and in the direction of E .
2. Field lines begin on positive charges and end on negative charges, or else go off to infinity.
3. Field lines do not cross one another.
4. To maintain a notion of scale within a diagram, the number of field lines starting or ending on a charge must be proportional to that charge.

Question 22

What is a continuous charge?

Answer 22

where charge is spread out over regions of space in a continuous or smooth manner

Question 23

What is volume charge density and its formula?

Answer 23

Firstly, suppose you have some charge which is continuously
distributed over some volume in space. We can then associate a scalar field with this volume of space called the volume charge density or simply charge density, denoted by the symbol ρ, which assigns a number with units of C m^−3 to each point in the space,
the charge per unit volume
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q = ρV - Total charge of a uniform volume charge distribution
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ρ =q/V -Uniform volume charge density

Question 24

What is surface charge density and its formula?

Answer 24

In the case of two-dimensional surfaces we can speak about charge per unit area or surface charge density, denoted by the symbol σ which assigns a number with units of C m^−2 to each point in the surface. If the charge distribution over a surface is uniform so that σ is a constant over the surface area A of the charge distribution, then we can determine that total charge q in the distribution by the following expression:

q = σA - Total charge of a uniform surface charge distribution

σ = q/A - Uniform surface charge density

Question 25

What is line charge density and its formula?

Answer 25

For the case of charge being continuously distributed on one-dimensional lines, we can speak about the charge per unit length or line charge density, denoted by the symbol λ which assigns a number with units of C m^−1 to each point in the line. If the charge distribution over the line is uniform so that λ is a constant over the length L of the charge distribution, then we can determine that total charge q in the distribution by the following expression:

q = λL - Total charge of a uniform line charge distribution

λ = q/L - Uniform line charge density

Question 26

Conductors, Insulators and electric currrent

Answer 26

The insulators are then collections in which no electric charge is free to move around. In contrast, conductors are collections in which there is some electric charge which is free to move around, and it
will do so if an external electric field is introduced. The ordered motion of charged matter within a conductor due to an electric field is called an electrical current.

Question 27

What are some examples of conductors?

Answer 27

Metals: The so-called conduction electrons are free to move around the metal. The positive metal ions which donate the conduction electrons to the ‘electron sea’ remain fixed in position.

Ionic solutions: These are liquids which have charged ions within them. These ions are free to migrate.

Plasma: These are gases which have been ionized, so that there are free positive ions and electrons that can move around.

Such as wood, glass and placstic

Question 28

What are the properties of solid conductors?

Answer 28

1. The electric field everywhere inside the conductor is zero. If this were not the case, free electrons within the conductor would be experiencing a force due to the nonzero field, and would therefore start moving in contradiction to the definition of equilibrium.
2. All electrical charge must reside on the surface of the conductor.
3. The electric field at the surface of the conductor must be normal (perpendicular) to that surface. If this were not true then there would be some component of the electric field which is directed parallel to the surface, which would cause the free electrons on the surface to move, a contradiction with the definition of equilibrium.
4. Charge tends to accumulate at sharp points of the conductor.

Question 29

Define surface and closed surface

Answer 29

Closed Surface: Which means that the imagined surface fully encloses or surrounds some finite volume of
space. In the case of a closed surface, the surface can have no holes or edges.

Question 30

Define Gaussian Surface

Answer 30

A Gaussian surface is any imagined closed surface, and so has a finite surface area, with the convention is that the positive
direction is from the inside to the outside of the closed surface.

Question 31

Define surface with orientation or orientated surface

Answer 31

A surface with an orientation – also known as an orientated surface – is an imagined surface where you have also decided which direction through the surface is to be called positive and which direction is to be called negative.

Question 32

Electric Flux and Gaussian surfaces

Answer 32

REFER TO DOCUMENT FOR EXAMPLES

Question 33

What is the formula for any Gaussian surface the total electrical flux ΦE passing outward through the surface?

Answer 33

ΦE = qenclosed / e0

Note: Gaussian surface the total magnetic flux ΦB passing outward through the surface is given by: ΦB = 0

Question 34

What is the formula for the strength of an electric field?

Answer 34

|ΦE| = EA .
Note: the equation does not take into account the orientation of the surface. If the orientation of the surface is in the same direction as the field lines then the flux would be positive. In contrast, if the orientation of the surface is in the opposite direction to the field lines then the flux would be negative.

Question 35

What is the formula for the number of field lines passing through the surface has decreased and the flux through the surface?

Answer 35

ΦE = EA cos θ

Question 36

What are the properties of an Area Vector?

Answer 36

1. The area vector is perpendicular to the flat surface and points out of the surface inthe direction of positive orientation.
2. The magnitude of the area vector is equal to the area of the flat surface A

Question 37

What is the formula of flux through a flat surface and the three special cases?

Answer 37

ΦE = E · A = EA cos θ, where E and A are vectors

If the area vector and the constant electric field both point in the same direction we have θ = 0 and so ΦE = EA.

If the area vector and the constant electric field point in opposite directions we have θ = π and so ΦE = −EA.

If the area vector is perpendicular to the constant electric field we = have θ = π/2 and so ΦE = 0, and no flux passes through the surface since it is parallel to the field.

Question 38

What are the steps to compute the total flux through a surface from the electric field?

Answer 38

1. Conceptually break the entire surface into tiny (infinitesimal) patches. These patches are so small that they are effectively flat, even if the overall surface is curved. (For example, think about breaking the surface of the Earth into small patches, if the patches are small enough they are all approximately flat.)
2. For each of the tiny flat patches we now associate an area vector denoted by dA. This area vector must be perpendicular to the patch, point in the direction of positive orientation of the surface, and have a magnitude dA which is equal to the area of the patch.
3. Now compute the electric flux dΦE through each of the tiny patches by calculating dΦE = E~ · dA~, where E~ is the value of the electric field at the point in space where the patch is located, and dA~ is the patch’s area vector. The value of E~ will, in general, be different for different patches but since the patches are so small the value of E~ will be constant over the patch.
4. Now compute the flux through the entire surface by adding together the flux dΦE through each of the tiny patches. Since the process involves infinitesimals, we will perform an integral over the entire surface rather than a summation over all patches.

Question 39

What is Gauss Law and its formula?

Answer 39

Given by: ∫E · dA = qenclosed / e0, where E and A are vectors

Question 40

What is the formula for Electric field outside of a charged sphere?

Answer 40

E = (1/(4pie0)) * (q/r^2) * r(vector)

Question 40

What is the formula for Gauss’s Law for Magnitism?

Answer 40

∫B · dA = 0 where, B and A are vectors

Question 41

What is the formula for Electric field due to a charged line?

Answer 41

E = λ / (2π *e0 *r)

Question 42

What is the formula for Electric field due to a charged sheet?

Answer 42

E = σ / 2* e0

Question 43

What is the formula for Electric field due to a conducting charged sheet?

Answer 43

E = σ / e0

Question 44

What is the formula for amount of work that the field does

Answer 44

dW = F · dl = q0E · dl , where F, l and E are vectors

Question 45

Define conservative force

Answer 45

Means that the work it does when a test charge moves from a point a to another point b is independent of the path taken in moving from a to b.

Question 46

What is eletrcial potential difference and its formula?

Answer 46

The electrical potential difference – or simply the potential difference – between the points a and b, which is denoted by ∆V = Vb − Va, is defined to be the change in potential energy per unit charge of a test charge as it is moved from a to b and is given by ∆V = ∆U / q0 = b∫a E · dl, where E and L are vectors

Question 47

What is the formula for Potential difference between parallel plates?

Answer 47

∆V = Qd / e0 *A

Question 48

What is a capacitor and its formula?

Answer 48

a capacitor consists of any two charged conductors which are separated by some distance and carry opposite charges. If the size of the potential difference between the two oppositely charged conductors is denoted by V and the size of the charge each conductor holds is Q, then the capacitance, C, is defined to be C = Q / V

Question 49

What is the formula for parallel plate capacitor?

Answer 49

C|| = Q / ∆V = e0*A / d

Question 50

What is the zero of the electrical point?

Answer 50

it is convenient to simply declare some particular point in space to be the zero value of the electrical potential. This has no physically measurable consequences but turns out to be extremely useful.

Question 51

What is the formula for point charge potential

Answer 51

V(r) = (q/(4pie0)) * (1/r) or V(x,y,z) = (q/(4pie0)) * (1/sqrt(x^2+y^2+z^2))

Question 52

What is the formula for the electrical potential of a charge distribution?

Answer 52

V(r) = (q/(4pie0)) * (sum qi / ri)

Question 53

How can energy be stored - energy density and give the formulas (energy stored in a charged capacitor and energy density)?

Answer 53

energy can be considered to be stored directly within the electric field itself. As all electric fields associated with charge distributions store energy.

Since the field is not localised and is spread out over space – usually with different strengths at different points – we can really only meaningfully talk about the energy density of a field, which is the energy per unit volume of the field. This energy density will vary from place to place depending on the size of the electric field strength at each location.

U = 1/2 * CV^2 - Energy stored within a charged capacitor

ue = 1/2 * e0 * E^2