CK-12-Physics - Intermediate

16.2. Electric Potential http://www.ck12.org

Other Units for the Electric Field

The electric field has unitsNC, since

−→

E=

−→F
q. But the electric field has been also defined using the scalar equation
V=Ex. Transposing terms, the electric field isE=Vx. So the units of the electric field can be also expressed as
volts per metermetervolts→Vm.
If we compare the units for the electric fieldNCandVm, we see that a(N∗m)is equivalent to a(C∗V). A Joule can
therefore be expressed as a Coulomb-Volt. Recall that work, measured in Joules, is the product of charge and voltage
W=q∆V.

Illustrative Example 16.2.1

All questions refer toFigure16.5.

a. What is the potential atx= 2. 0 cm? The electric field isE= 25. 0 NC.

Answer:

The potentialVvaries directly with the positionxbetween the plates(V=Ex). Thus,V= 25. 0 NC( 2. 0 × 10 −^2 m) =

0. 50 V.

b. Sketch a graph showing the relationship between the potential and the position.

Answer:

c. How much work is done by an external forceFmoving a− 2. 0 × 10 −^6 Ccharge from the positive plate to the

negative plate?

Answer:An external force must pull the charge away from the positive plate so the force will be in the same direction

as the displacement.

W=q(Vf−Vi) = (− 2. 0 × 10 −^6 C)( 0. 00 V− 1. 50 V) = 3. 0 × 10 −^6 J

d. What is the magnitude of the Coulomb force acting on the charge?

Answer:

W=F×→ 3. 0 × 10 −^6 J=F( 6. 00 × 10 −^2 m)

F=

3. 0 × 10 −^6 J

6. 00 × 10 −^2 m

= 5. 0 × 10 −^5 N