Question

An electric dipole has a fixed dipole moment $p$, which makes angle $\theta$ with respect to the x-axis. When subjected to an electric field $E_1=E_i$, it experiences a torque $T_1=\tau k$. When subjected to another electric field $E_2=\sqrt{3}{E}_{1}j$ it experiences a torque $T_2=-T_1$ .The angle $\theta$ is:

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is C

${60}^{\circ }$

Step1. Given data :

dipole moment$=$ $p$

electric fields$=E_{1}and{E}_2$

Torque$=T_{1}and{T}_2$

Step 2. Find the torque of the electric fields:

$p=p\cos {\theta }_i+p\sin {\theta }_j$

$E_1=E_i$

$T_1=p\times E_1=(p\cos {\theta }_i+p\sin {\theta }_j)\times E_i$

$\tau k=pE\sin \theta (-k)-\left(i\right)$

$E2=\surd 3E1j$

$T2=(p\cos \theta i+p\sin \theta j)x\surd 3E1j$

$–\tau k=\surd 3pE1\cos \theta k—–\left(ii\right)$

Step 3. find the angle theta:

$From\left(i\right)and\left(ii\right)$

$pE\sin \theta =\surd 3pE\cos \theta$

$\tan \theta =\surd 3$

$\theta ={60}^{\circ }$

Hence ,option (C) is correct.