2. Equipotential Surface
E-field
Equipotential Surface
2 Point Charges
Uniform Electric Field
Point Charge
Using equipotentials instead of fields can make solving problems much easier – equipotential is a scalar quantity, whereas the field is a vector. Equipotentials are similar to contour lines on a map.

3. Equipotential Surface
Notes on Equipotential Surfaces
1) Equipotential surfaces are always perpendicular to Electric Field lines
2) If a charge moves on an equipotential surface, the work done by the Electric Field is zero, as there is no change in potential & cosθ=90o F
Equipotential Surface
E-Field + s
6V V V V V V
3) Equipotential surfaces can never cross
4) Equipotential surfaces are spaced according to field strength.

4. Do you understand these diagrams?

5. Potential gets higher in this direction
In the case of a Uniform Electric Field (parallel plate capacitor), it is especially easy to calculate the potential difference between equipotential surfaces:
10V V V V V V
++++
---- E
Potential gets higher in this direction
Potential gets lower in this direction
Let V = 10 V
d = 10 cm
E = 10/0.1
= 100 V/m

6. The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid black. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I.
1) At which of the labeled points will the electric field have the greatest magnitude?
A)G B)I C)A D) H E) D
2) At which of the labeled points will an electron have the greatest potential energy?
A)A B)D C)G D) H E) I
3) What is the potential difference between points B and E?
A)10 V B)30 V C)40 V D) 50 V E) 60 V

7. 4) What is the direction of the electric field at B?
A) toward A B) toward D C) toward C D) into the page
5) How much work is required to move a –1 µC charge from A to E?
+3.0 x10–5 J B) –4.0 x10–5 J C)+7.0 x10–5 J D) zero
6) How much work is required to move a –1 µC charge from B to D to C?
+2.0 x 10–5 J B) –2.0 x 10–5 J C) +4.0 x 10–5 J D) zero
7) A positive point charge is placed at F. Complete the following statement: When it is released,
A) no force will be exerted on it.
B) a force will cause it to move toward E.
C) a force will cause it to move toward G.
D) a force will cause it to move away from E.
E) it would subsequently lose kinetic energy.
8) What is the magnitude of the electric field at point A?
10 V/m B) 25 V/m C) 30 V/m D) 75 V/m E)100 V/m
9)A point charge gains 50 mJ of electric potential energy when it is moved from point D to point G. Determine the magnitude of the charge.
A) 1.0 mC B) 1.3 mC C) 25 mC D) 50 mC E)130 mC