Two point charges, 6.0 µC and -2.0 µC, are placed 5.0 cm apart on the x axis, su

Question

Two point charges, 6.0 µC and -2.0 µC, are placed 5.0 cm apart on the x axis, such that the -2.0 µC charge is at x = 0 and the 6.0 µC charge is at x = 5.0 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

a )

using equation and substitutng the values

k X 6 X 10-6 / ( X - 0.05 )2 = k X 2 X 10-6 / X2

6 X 10-6 / ( X - 0.05 )2 = 2 X 10-6 / X2

6 / ( X - 0.05 )2 = 2 / X2

6 X2 = 2 ( X2 + 0.0025 - 0.1 X )

4 X2 + 0.2 X - 0.005 = 0

X = 0.0183 m = 18.3 cm

X = - 0.0683 m = - 6.83 cm ( correct distance )

X < 0

b )

k X 6 X 10-6 / ( X - 0.05 ) = k X 2 X 10-6 / X

6 / ( X - 0.05 ) = 2 / X

6 X = 2 X - 0.1

4 X = 0.1

X = 0.025 cm

X = 2.5 cm

0 < X < 5 cm

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