Question

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

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

Answer 1

Answer: (B)

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