An electric dipole has a fixed dipole moment $\overrightarrow{\mathrm{p}}$, which makes angle $\theta$ with respect to $x$-axis. When subjected to an electric field $\overrightarrow{\mathrm{E}}_{1}=\mathrm{E} \hat{i}$, it experiences a torque $\overrightarrow{\mathrm{T}}_{1}=\tau \hat{k}$. When subjected to another electric field $\overrightarrow{\mathrm{E}_{2}}=\sqrt{3} \mathrm{E}_{1} \hat{j}$ it experiences a torque $\overrightarrow{\mathrm{T}}_{2}=-\overrightarrow{\mathrm{T}}_{1}$. The angle $\theta$ is :

JEE Main · 2017 · 02 Apr 2017 · Offline · Electrostatics

An electric dipole has a fixed dipole moment

p

, which makes angle

θ

with respect to

x

-axis. When subjected to an electric field

E_{1} = E \hat{i}

, it experiences a torque

T_{1} = τ \hat{k}

. When subjected to another electric field

E_{2} = 3 E_{1} \hat{j}

it experiences a torque

T_{2} = - T_{1}

. The angle

θ

is :

Answer: (A)

Write the dipole as

p = p cos θ \hat{i} + p sin θ \hat{j}

. In

E_{1} = E \hat{i}

the torque is

p \times E_{1} = pE sin θ \hat{k}

, so

τ = pE sin θ

. In

E_{2} = 3 E \hat{j}

the torque is

- 3 pE cos θ \hat{k}

. The requirement

T_{2} = - T_{1}

forces

3 pE cos θ = pE sin θ

, i.e.

tan θ = 3

, so

θ = 6 0^{\circ}

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option