Electric Potential and Potential Energy: Definitions, Formulas, and Examples, Slides of Physics

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8. Potential and potential energy and examples

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Potential (gravitational) energy and force:

U = −

Potential energy

⊙

𝑠𝑝𝑎𝑐𝑒

𝑒𝑎𝑟𝑡ℎ

𝑒𝑎𝑟𝑡ℎ

𝑠𝑝𝑎𝑐𝑒

www.s-cool.co.uk

Potential (electric) energy

and force:

U =

Electric potential energy

𝐵

𝐴

𝐴

𝐵

A

B

Potential (electric)

and electric field:

V =

Electric potential between A and B

(or voltage between A and B)

𝐵

𝐴

𝐴

𝐵

A

B

E and V for an Infinite Sheet of Charge

The equipotential lines are the dashed blue

lines.

The electric field lines are the brown lines.

The equipotential lines are everywhere

perpendicular to the field lines.

Section 25.

V

A

V

B

𝐵

𝐴

𝐴

𝐵

d

Example 0: potential of a uniform electric field

line integral (follow any line)

E and V for an Infinite Sheet of Charge

The equipotential lines are the dashed blue

lines.

The electric field lines are the brown lines.

The equipotential lines are everywhere

perpendicular to the field lines.

Section 25.

V

A

V

B

𝐵

𝐴

𝐴

𝐵

d

𝑥

x

Example 0: potential of a uniform electric field

In general:

line integral

An isolated positive point charge produces

a field directed radially outward.

The potential difference between points A

and B will be

B A e

B A

V V k q

r r

Section 25.

Example 1: potential of a point charge

The electric potential is independent of the path between points A and B.

It is customary to choose a reference potential of V = 0 at r

A

Then the potential due to a point charge at some point r is

e

q

V k

r

Section 25.

Example 1: potential of a point charge

Van de Graaff Generator

Charge is delivered continuously to a high-

potential electrode by means of a moving

belt of insulating material.

The high-voltage electrode is a hollow

metal dome mounted on an insulated

column.

Large potentials can be developed by

repeated trips of the belt.

Protons accelerated through such large

potentials receive enough energy to initiate

nuclear reactions.

Section 25.

What is the potential at the surface of the Van de Graaff generator?

A. 1 - 10V

B. 10 - 100V

C. 100 - 1kV

D. 1kV-10kV

E. 100kV-1MV

F. 1MV-10MV

How would you determine the potential at the surface of the Van de

Graaff?

The Van der Graaff experiment to

determine the electrostatic potential𝑽

𝒂

𝟎

Breakdown electric field in air is

d

(assuming a uniform

electric field between

the two spheres)