A point charge of is fixed at on the -axis

PHYSICS · Multi-part · CBSE · Physics · Electric Charges and Fields · Electric Charges and Fields

Problem

A point charge of

+4.0\,\mu\text{C}

is fixed at

x=-0.15\,\text{m}

on the

x

-axis, while an equal-magnitude charge of

-4.0\,\mu\text{C}

is fixed at

x=+0.15\,\text{m}

. The potential at infinity is defined to be zero. (a) Obtain an explicit expression for the electric potential

V(x)

at an arbitrary point on the

x

-axis produced by the two charges. (b) Determine analytically all point(s) on the

x

-axis where the net electric potential is exactly zero. Provide complete algebraic justification, including the solution of any equations required. (c) Classify each solution obtained in part (b) as being located between the charges or outside the charges, and explain why no other solution(s) exist on the

x

-axis. (d) For each point where

V=0

, calculate the magnitude of the electric field

E

at that location. Discuss whether the condition

V=0

necessarily implies

E=0

in this configuration.

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