Two identical point charges are fixed on the –axis at positions and

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

Problem

Two identical point charges

+q

are fixed on the

x

–axis at positions

x=-a

and

x=+a

. Consider points only along the

x

–axis. (a) Derive an expression for the electric potential

V(x)

at an arbitrary point

x

on the

x

–axis (take

V \to 0

|x| \to \infty

). (b) From your result in part (a), obtain an algebraic expression for the electric field

E(x)

along the

x

–axis. Clearly indicate the region(s) of

x

for which the expression is valid. (c) Evaluate the magnitude of the electric field at the midpoint

x=0

using the expression from part (b), and interpret the physical significance of this result. (d) For the specific numerical values

q = 2.0\,\mu\text{C}

and

a = 4.0\,\text{cm}

, calculate the electric field magnitude at

x = 8.0\,\text{cm}

. State the direction of the field at that point.