Question

An electric dipole consists of two equal and opposite charges placed $2\, cm$ apart. When the dipole is placed in a uniform electric field of strength $10^{5} NC ^{-1}$, it experiences a maximum torque of $0.2 \times 10^{-3} N m$. Find the magnitude of each charge.

• A. $20\, \mu C$
• B. $10\, \mu C$
• C. $15 \,\mu C$
• D. $40 \,\mu C$

Answer 1

Answer: (B)

Here, $2 \,a=2 \,cm =0.02 \,m , \tau_{\max }$
$=0.2 \times 10^{-3} Nm$
and $E=10^{5} NC ^{-1}$.
Now, maximum torque on the dipole,
$\tau_{\max }=p E=q(2 a) \times E$
$\therefore q=\frac{\tau_{\max }}{(2 a) E}$
$=\frac{0.2 \times 10^{-3}}{0.02 \times 10^{5}}$
$=10^{-7} C =10\, \mu C$