CK-12-Physics - Intermediate

http://www.ck12.org Chapter 16. Electric Potential

Electric Potential Difference in a Uniform Electric Field

In working with the change in potential energy above, we wrote the equation

∆PE=qExf−qExi=qE(xf−xi)→Let us call this Equation A.

Recall that the electric potential was defined at a specific pointVx 1 =PEqx^1.

We therefore see thatPEx 1 =qVx 1 →Let us call this Equation B.

Comparing Equation A and Equation B, we see that the electric potential can be expressed asVx 1 =Ex 1. If the electric

potential is defined asV=0 atx=0, then the potential at any point in the electric field isV=Ex. (Assuming that

vectorEis directed along thex−axis).

Note: It is common to writeV=Ed, whereVis understood to mean the voltage (or potential difference) between

the plates of a parallel-plate conductor, anddis the distance between the plates.

Check Your Understanding

Verify that the potential difference between the plates inFigure16.5 is 1.5V. Recall that the electric field isE=

25. 0 NC.

Answer:V=Ed=

(

25 NC

)

( 6. 00 × 10 −^2 m− 0. 00 m) = 1. 5 V

Work

We state again:

1. The electric potential is defined as the energy per unit charge→Vx 1 =PEqx^1.


2. The electric potential difference (the voltage) isVf−Vi=PEqf−PEqi


3. An arbitrary reference level must be established for zero potential (just as in the case of gravitational potential
   energy).


4. The units of electric potential and electric potential difference areCJsinceVx 1 =
   PEx 1
   q.

It is often useful to express the voltage in terms of the work done on a charge.
FromVf−Vi=PEqf−PEqi, we havePEf−PEi=q(Vf−Vi)→∆PE=q(Vf−Vi).
But the work done on a charge by the field isWf ield=−∆PE.
Combining∆PE=q(Vf−Vi)andWf ield=−∆PEgivesWf ield=−q(Vf−Vi).
An external force that does work on a charge in an electric field exerts a force in the opposite direction to the field
(just as the external force acting on a spring acts opposite to the spring force). The work that an external force does
is thereforeWexternal f orce=q(Vf−Vi).
The voltage can be thought of as the amount of work done by the electric field per unit charge in moving a charge
between two points in the electric field∆V=Wq.
We often refer to a change in potential as simply “the voltage.”
In computing the work, it is often easier to ignore the sign in the equation and simply see if the force and displacement
on the charge are in the same direction (positive work) or opposite to one another (negative work). Recall that the
force and displacement need not be in the same direction or oppositely directed. In general, work is expressed as
W=F xcosθ

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