An isolated point charge is located somewhere on the -axis

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

Problem

An isolated point charge

q

is located somewhere on the

x

-axis. A student measures the electric potential (relative to infinity) at two points

P

and

Q

on the same axis and records the values

V_{P}

and

V_{Q}

. No other charges are present. (i) Write the expressions for

V_{P}

and

V_{Q}

in terms of

q

and the respective distances

r_{P}

and

r_{Q}

from the charge. (ii) Explain why the ratio

\dfrac{V_{P}}{V_{Q}}

depends only on the distances

r_{P}

and

r_{Q}

and not on

q

. (iii) Using the above fact, justify why two independent potential measurements are sufficient to determine both the magnitude of

q

and its position on the axis.