Two identical point charges

PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance

Problem

Two identical point charges, each of magnitude

+6.0\,\mu\text{C}

, are fixed on the

x

-axis at positions

x=-0.30\,\text{m}

and

x=+0.30\,\text{m}

. The electric potential is defined to be zero at an infinite distance from the charges. (a) Derive an expression for the electric potential

V(x)

at an arbitrary point on the

x

-axis. Express your answer in terms of

x

, fundamental constants, and the given quantities. (b) Let

V_{0}

be the electric potential at the origin. Determine all coordinate(s)

x

on the

x

-axis (excluding

x=\pm 0.30\,\text{m}

) where the potential equals

\tfrac12 V_{0}

. Show all algebraic steps that lead to your result. (c) Evaluate the numerical value(s) of the coordinate(s) found in part (b). State each answer with an appropriate sign and in meters. (d) Interpret the physical significance of the point(s) you found. In particular, discuss whether a small positive test charge placed at each location would experience a net electric force of zero or not, and explain your reasoning.

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