Two point charges, 3.0 µC and -2.0 µC, are placed 4.2 cm apart on the x axis, su

Question

Two point charges, 3.0 µC and -2.0 µC, are placed 4.2 cm apart on the x axis, such that the -2.0 µC charge is at x = 0 and the 3.0 µC charge is at x = 4.2 cm.

(a) At what point(s) along the x axis is the electric field zero? (If there is no point where E = 0 in a region, enter "0" in that box.)

(b) At what point(s) along the x axis is the potential zero? Let V = 0 at r = . (If there is no point where V = 0 in a region, enter "0" in that box.)

Explanation / Answer

Part a

q1 = 3.0 C, at x1 = 4.2 cm, q2 = -2.0 C, at x2 = 0

a) at x < 0, E = 0

E = kq1/(x1 - x)2 - k|q2|/(x2 - x)2 = 0

3.0/(4.2 - x)2 = 2.0/x2

(4.2 - x)/|x| = (3.0/2.0) = 1.5

(4.2 + |x|)/|x| = 1.5

4.2/|x| + 1 = 1.5

|x| = 4.2/(1.5 - 1) = 18.7 cm

answer: x = -18.7 cm

Part b

at x, V = 0

V = kq1/|x1 - x| - k|q2|/|x2 - x| = 0

3.0/|4.2 - x| = 2.0/|x|

|(4.2 - x)/x| = 3.0/2.0 = 1.5

i) if 0 < x < 4.2, (4.2 - x)/x = 1.5, 4.2/x - 1 = 1.5, x = 1.68 cm

ii) if x < 0, (4.2 + |x|)/|x| = 1.5, 4.2/|x| = 1.5 - 1 = 0.5, |x| = 8.4 cm

so x = -8.4 cm

iii) if x > 4.2, (x - 4.2)/x = 1.5, x - 4.2 = 1.5x, no solution.

so x = 1.68 cm or -8.4 cm

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