Question

An electric dipole placed in an electric field of intensity 2 × 10⁵ N/C at an angle of 30° experiences a torque equal to 4 Nm. The charge on the dipole of dipole length 2 cm is

(a) 7 µC

(b) 8 mC

(c) 2 mC

(d) 5 mC

Answer 1

Correct option is (c) 2 mC

dipole moment P = lq

P = 0.02 x q

Torque

 \(\vec{T}=\vec{p}\times\vec{E}\)

4 = 0.02q x 2 x 10⁵ sin 30°

4 = 0.02q x 2 x 10⁵ x 1/2

\(q = \frac{400}{0.02\times10^5}\)

q = 200 x 10^-5

q = 2mc

Answer 2

Correct option is (c) 2 mC

q = \(\tau\)/[(2a)E sin θ] = \(\frac{4}{2\ \times\ 10^{-2}\ \times\ 2\ \times\ 10^{-5 }sin\ 30°}\)

= 2 x 10^-3 C = 2mC