9.3 – Electric Potential

Electric Potential Energy uniform fields

The more we move a charge from A towards B, the more Potential Energy it has.

The Potential Energy will be equal to the work done:

h 𝐸=𝐹𝑞

𝑊= h𝑞𝐸 𝑃𝐸= h𝑞𝐸Electric Potential Energy

𝑃𝐸= h𝑚𝑔Gravitational PE

This is just like:

Electric Potential (V) uniform fields

All points in a field have a Potential. It is the energy a coulomb’s worth of charge would have if placed at that point.

Field Lines

Lines of Equipotential

1. What’s the Potential Difference (pd) between: a) A & C? b) B & D?2. If a Charge of +3C is placed at B, how much PE does it have?3. If a charge of +2C is moved from C to B, how much work would be done? What about -2C?4. If a charge of +3C was placed at B and released, what would it do? How much KE would it

have at A?

Potential Gradient (V) and Field Strength (E)Uniform Fields:Just like with Gravitational fields the Electric Field Strength is the same as the Potential Gradient for the sort of uniform field you get between two electrodes.

𝐸=∆𝑉∆h

Electric Potential (V) at a point is the amount of work per unit charge needed to take a small positive test charge from a place of zero potential (infinity) to the point.

Electric Potential definition

Potential (V)

𝐸=∆𝑉∆h

This image shows the Electric Potential around chargesand draws it as an equipotential surface.

It is easy to see what will happen to a positive charge if it is placed somewhere on this surface.

Electric Fields and Charges behave just like Gravitational fields and Masses, the only real difference is that they can attract AND repel.

+

+-

-

Equipotential simulations

Vector Fields Applet Electrostatics Applet

http://www.falstad.com/emstatic/ http://www.falstad.com/vector3de/

For both simulations click in the drop down box and change it to equipotential. Then shoose different scenarios to see the equipotential lines

CLICK ON THE PICTURES if the links don’t work

Lines of Equipotential (V)

Around graphene atoms there are ‘valleys’ of equipotential that electrons can flow through, giving the material really unusual electrical properties.

If the electron is moving along an equipotential it is doing no work.

Electrical current with no resistance ? At room temperature?

Click on the pictures for more info

GrapheneThe 2010 Nobel prize for Physics was awarded to Andre Geim and Konstantin Novoselov of the University of Manchester (UK) for their experiments with Graphene.

Potential due to a point chargeThe Potential at point P is defined as the amount of work per unit charge needed to take a small POSITIVE test charge from a place of zero potential (infinity) to P.

-W-Q

P has a +ve potential (+V)

P has a -ve potential (-V)

Potential due to a point charge continued

𝐹=𝑘𝑄𝑞𝑟2

𝑉=𝑘𝑄𝑟

The first graph represents the Force as the +ve test charge moves from ∞ to P.

The area under the graph is the Work Done and this allows us to use calculus to get the Potential (V) graph and Equation.

Addition of Potential

Potential is a ScalarJust add the potential from each charged body to find the combined potential.

𝑉=𝑘𝑄1

𝑟1+𝑘−𝑄2

𝑟1

Extra clevernessAt P there might be zero potential but that doesn’t mean there is zero field.

A +ve charge will move to the right if placed at P so there must still be a field.