Question

An electric dipole is placed at an angle of $45^{\circ }$ with an electric field of intensity $10^{7}N{C}^{-1}$. It experiences a torque equal to $15\times 10^{2}N-m$. What will be magnitude of charge on dipole if it is $5cm$ long?

• A. $1mC$
• B. $2mC$
• C. $5mC$
• D. $4mC$

Answer 1

Answer: (B)

$\tau =\vec{p}\times \vec{E}$
$\tau =pE\sin \theta$
$\tau =q\times 2\ell \times E\times \sin \theta$
$q=\frac{\tau }{2\ell \times E\times \sin \theta }$
$\Rightarrow q=\frac{15\times 10^2}{2\times 5\times 10^{-2}\times 10^7\times \frac{1}{\sqrt{2}}}$
$q=\frac{15\sqrt{2}\times 10^2}{10\times 10^5}$
$15\sqrt{2}\times 10^{-4}$
$=2.121\times 10^{-3}$
$=2.121mC$