-3 V 3) (Adapted from problem by Kesten & Tauck) Equipotential lines for some re

Question

-3 V 3) (Adapted from problem by Kesten & Tauck) Equipotential lines for some region of space are shown in the figure at right. What is the electric field at a) point A? b) point B? 0 V IV -2V1-4V 0 m 1 m 2m 3 m 4 m c) Assume that a negative charge q=-20C is released from rest at point B; since it is negatively charged, it climbs "uphill V" toward the left, when it reaches the x = 0m line (which is at 0V), what is its kinetic energy? Note: In parts a) and b), you are estimating the electric field rather than computing it exactly.

Explanation / Answer

3. for the given equipotential lines in the give fingure

electric field is given by -dV/dx

a. at point A

electric field, E = -dV/dx = 1/2 = 0.5 V/m

b. at point B

electric field, E = -dV/dx = 2/1 = 2 V/m

c. CHANGE IN POTENTIAL BETWEEN B and A, dV = 3 - 1*0.5/2 = 3 - 1/4 = 2.75 V

hence

chang ein KE of the charge q = -2micro C

dE = qdV = 2.75*2*10^-6 = 5.5 micro J

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