Question

A charge situated at a certain distance along the axis of an electric dipole experience a force $F$. If the distance of the charge from the dipole is doubled, the force acting on it will become

• A. $2F$
• B. $\frac{ F}{ 2}$
• C. $\frac{ F}{ 4}$
• D. $\frac{ F}{ 8}$

Answer 1

Answer: (D)

$\frac{ F}{ 8}$

Answer 2

The electric field at a point distance r from electric dipole is
E = $\frac{ 1}{ 4 \pi \varepsilon_0} . \frac{ 2p}{ r^3 }$ \hspace20mm ..( axial line)
where pis dipole moment and ris the distance of charge from centre of dipole.
or $E \propto \frac{ 1}{ r^3 }$
Force on charge is
F = QE
or $F \propto \frac{ 1}{ r^3 }$
$\therefore \frac{ F_2 }{ F} = \bigg( \frac{ r }{ 2r } \bigg)^3 = \frac{ 1}{ 8 }$
or $F_2 = \frac{ F}{ 8}$