JEE Main Solved Paper 2017 Question 10
Question: An electric dipole has a fixed dipole moment $ \vec{p}, $ , which makes angle $ \theta $ with respect to x-axis. When subjected to an electric $ {{\vec{E}}_1}=E\hat{i}, $ field It experiences a torque $ \vec{T}=\tau \hat{k}. $ When subjected to another electric field $ {{\vec{E}}_2}=\sqrt{3}E _1\hat{j} $ it experiences torque $ {{\vec{T}}_2}=-{{\vec{T}}_1}. $ The angle $ \theta $ is: [JEE Main 2017]
Options:
A) $ 60^{o} $
B) $ 90^{o} $
C) $ 30^{o} $
D) $ 45^{o} $
Show Answer
Answer:
Correct Answer: A
Solution:
- So from $ \vec{\tau }=\vec{p}\times \vec{E} $ $ \tau \hat{k}-\tau \hat{k}=( p _{x}\hat{i}+p _{y}\hat{j} )\times ( E\hat{i}+\sqrt{3}E\hat{j} ) $ $ =p _{x}\sqrt{3}E\hat{k}+p _{y}E( -\hat{k} ) $ $ 0=E\hat{k}( \sqrt{3}p _{x}-p _{y} ) $ $ \frac{p _{y}}{p _{x}}=\sqrt{3} $
$ \therefore $ $ \tan \theta =\sqrt{3} $ $ \theta =60^{o} $
