Physics

Problem

A point charge

q_{1}=+12\,\mu\text{C}

is kept in air. It is replaced by another charge

q_{2}

that is submerged entirely in a non-conducting oil of relative permittivity

\varepsilon_{r}=5

, such that the electric potential at a point

0.40\,\text{m}

from the charge remains unchanged. a. (i) Obtain an expression relating

q_{2}

q_{1}

and

\varepsilon_{r}

so that the potential at the specified point is the same in both cases. b. (ii) Calculate the value of

q_{2}

required. c. (iii) For each case (with

q_{1}

in air and

q_{2}

in oil), compare the magnitudes of the electric field at the same

0.40\,\text{m}

point. Explain the reason for any difference.