The electric force between two point charges separated by a certain distance d in air is F.The distance at which they should be placed in a medium of relative permittivity k so that the force remain the same is

Question

The electric force between two point charges separated by a certain distance d in air is F.The distance at which they should be placed in a medium of relative permittivity k so that the force remain the same is (A) d (B) (d/k) (C) kd (D) (d/√k)

Tardigrade Admin · Accepted Answer

Electric force between two point charges

q_{1}

and

q_{2}

separated by a distance d in air is given by

F = \frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{d ^{2}}

...(i)
Electric force between two point charges

q_{1}

and

q_{2}

separated by a distance

d^{'}

in a medium of relative permittivity

k

is given by

F^{'} = \frac{1}{4 π E _{0} k} . \frac{q _{1} q _{2}}{d ^{' 2}}

According to question

, F = F^{'}

∴ \frac{1}{4 π e _{0}} \frac{q _{1} q _{2}}{d ^{2}} = \frac{1}{4 π e _{0} k} \frac{q _{1} q _{2}}{d ^{' 2}}

\frac{1}{d ^{2}} = \frac{1}{k d ^{' 2}}

or

k d^{' 2} = d^{2}

or

d^{'} = \frac{d}{k} .

Q. The electric force between two point charges separated by a certain distance d in air is F.The distance at which they should be placed in a medium of relative permittivity k so that the force remain the same is

$d$

$\frac{d}{k}$

$k d$

$\frac{d}{k}$

Q. The electric force between two point charges separated by a certain distance d in air is F.The distance at which they should be placed in a medium of relative permittivity k so that the force remain the same is

d

kd​

kd

k​d​

$d$

$\frac{d}{k}$

$k d$

$\frac{d}{k}$