Notes - Electric Field & Potential

IB Assessment Statements

 _{Electric Potential Difference}

 _{5.1.1. Define electric potential difference.}

 5.1.2. Determine the change in potential energy when a charge moves between two points at

different potentials.

 _{5.1.3. Define the electronvolt.}

Review

 _{In SL we learned:}

 _{The formula for the electric force between}

two point charges is

 _Or,

 _where

2 2 1 0 Q 4 1 = F r Q  2 2 1 Q k = F r Q 2 2 9 0 C 10 99 . 8 4 1 =

k  x N  m

Electric Field

 _{An electric field exists around any}

charged object and extends/radiates either into or out of the object

 _{By convention, charge flows from positive to}

negative so,

 _{For a positively charged object, the field lines}

Electric Field

 For a positively charged object, the field lines extend outward

 _{For a negatively charged object, the field}

lines extend inward

Electric Field

 _{Electric field is defined as the force per unit}

charge experienced by a small positive test

charge, q,

The electric field is a vector with direction being the same as the force a positive

charge would experience at the given point

Electric Field

 _{Units for electric field is N/C}

qE

F

q

F

E





Electric Field

 _{The electric field from}

a single point charge, Q, at a point a

distance r away is

Electric Field

 _{Likewise, the charge on the surface of}

a spherical conductor is given by

where R is the radius of the sphere. Inside the conductor the field is zero

2

R

Q

k

Electric Field Lines

 _{For a positively charged object, the field}

lines extend outward

 _{For a negatively charged object, the field}

lines extend inward

Electric Field Lines

 _{A convention for drawing field lines is}

that the number of field lines should be proportional to the strength of the

charge

 _{The stronger the electric field, the closer}

Electric Field Lines

 _{Field lines will flow toward opposite}

charges and away from like charges. For example, two equal and opposite

Electric Field Lines

Electric Field Lines

Electric Field Lines

 _{Uniform Electric Field exists when the}

field has a constant magnitude and

Electric Field Lines

 _{The field lines at the edges begin to curve}  _{The field is uniform if the length of the field}

Electric Potential

 _{Consider an electric field and a positive}

test charge q

 _{In order to move the charge from its}

Electric Potential

 _{If held in that new position, the test}

Electric Potential

 _{“V” is the electric potential and is}

defined in terms of the work, W, needed to bring a positive test charge, q, from very far away to a position close to the charged body

q

W

V



Remember that work is based on displacement and not distance

Electric Potential

 _{The unit of potential is:}

1V = 1J/1C

 _{The potential energy, U, is:}

E_p = qV

 _{The unit of potential energy is:}

Potential Difference

 _{The amount of work}

needed to move a

test charge from one point to another is equal to the change in potential energy of the charge

 _{Just like gravity}





Electronvolt

 _{Atomic physics deals with extremely small}

amounts of energy where the Joule is not really appropriate

 _{The electronvolt, eV, is equal to the work done}

when the charge on one electron is moved across a potential difference of 1 volt

Charge Moving In A Region of

Electric Potential

 _{A point charge moving in a region of an}

electric potential will have kinetic energy due to its mass and velocity

 _{It also has potential energy due to the electric}

potential

 _{As it moves through the region}

the potential impacts the

Charge Moving In A Region of

Electric Potential

 _{Law of Conservation of Energy states that the}

sum of the potential energy and kinetic

energy at one point must equal the sum of the potential energy and kinetic energy at any other point

B B

A

A

qV

mv

qV

mv







2

1

2

Electric Field between

parallel plates

 _{The electric field, E, between two parallel}

plates is equal to the potential difference between the plates, V, divided by the

distance between the plates, x

 Note that E is the electric field – E does not stand for energy!

x

V

E

How Does It Fall?

 Consider a positively charged metal sphere with some mass m

falling vertically through an electric potential

between two plates

 What is the direction of motion if it starts at point P?

 _{What is the direction of}

 When the sphere becomes charged, we know that the charge distributes itself evenly over the surface.

 Therefore every part of the material of the conductor is at the same potential.

 As the electric potential at a point is defined as being numerically equal to the work done in bringing a unit

positive charge from infinity to that point, it has a constant value in every part of the material of the conductor,

 Since the potential is the same at all points on the

conducting surface, then Δ V / Δx is zero. But E = - Δ V / Δ x.

From “Physics for the IB Diploma”

K.A.Tsokos (Cambridge University Press)

Gravitation Electricity

Acts on Mass (always +?) Charge (+ or -)

Force F = GM₁M₂/r2

Attractive only, infinite range

F = kQ₁Q₂/r2

Attractive or repulsive, infinite range

Relative strength 1 1042

Field g = GM/r2 _{E = kQ/r}2

Potential V = -GM/r V = kQ/r

Potential energy E_p = -GMm/r E_p = kQq/r

Objectives

 _{Appreciate that a charge q in an electric}

field of magnitude E will experience a force of magnitude

qE

Objectives

 _{Understand that the electric field of a}

point or spherical charge Q a distance r away has a magnitude of given by

and is radial in direction. The field is zero inside the charged conductor

2

r Q k

Objectives

 _{Understand that the electric field inside}

parallel plates is uniform and its magnitude is given by

Objectives

 _{Understand that the work done in}

moving a charge q across a potential difference



V

q

Objectives

 _{Understand that a charge q that is at a}

point where there is potential V will have an electric potential energy of

qV

Objectives

 _{Understand that a charge moving in an}

electric potential satisfies the law of conservation of energy,

B B

A

A

qV

mv

qV

mv







2

1

2