Points A and B lie within a region of space where there is a uniform electric field that has no x- or z-component; only the y-component Ey is non zero. Point A is at y=8.00 cm and point B is at y=15.0 cm. The potential difference between B and A is VB−VA=+12.0 V, so point B is at higher potential than point A. (a) Is Ey positive or negative? (b) What is the magnitude of the electric field? (c) Point C has coordinates x=5.00 cm, y=5.00 cm. What is the potential difference between points B and C?

(a) Ey is negative

(b) The magnitude of the electric field is E = 171.429 V/m

(c) The potential difference between points B and C is 17.1429 V

Explanation:

(a) Here, we have the potentials given by;

with point A at y = 8.00 cm and point B at point y = 15.0 cm

where point B is at a higher potential than point A, that is the electric potential is from;

B with y = 15.0 cm to A with y = 8.0 cm which means

decreases as y increases or  is negative.

(b) The magnitude of the electric field is given by

The work done to move a charge from B to A is

where

∴

E = 171.429 V/m

(c) Here we have point C x = 5.00 cm and y = 5.00 cm

Therefore we have the distance from B to C given by

Where 10.00 cm = 0.01 m

E = V/Δy

Therefore, V = Δy·E

For , Δy = and we have,