An electric dipole has a fixed dipole moment $\vec{p}$, which makes angles $\theta$ with respect to x-axis. When subjected to an electric field $\vec{E}_1 = E \hat{i}$, it experiences a
torque $\vec{T}_1 = \tau \hat{k}$. When subjected to another electric field $\vec{E}_2 = \sqrt{3 E_1} \hat{j}$ it experiences a torque $\vec{T}_2 = - \vec{T}_1$. The angle $\theta$ is
- $30^{\circ}$
- $45^{\circ}$
- $60^{\circ}$
- $90^{\circ}$
The Correct Option is C
Solution and Explanation
$\vec{E}_1 = E \hat{i}$
$\vec{T}_1 = \vec{p} \times \vec{E}_1$
$ = (p \cos \theta \hat{i} + p \sin \theta \hat{j} ) \times E (\hat{i})$
$\tau \hat{k} = p E \sin \theta (- \hat{k})$ ......(i)
$\vec{E}_2 = \sqrt{3} E_1 \hat{j}$
$\vec{T}_2 = (p\cos \theta \hat{i} + p \sin \theta \hat{j} ) \times \sqrt{3} E_1 \hat{j}$
$ - \tau \hat{k} = \sqrt{3} p E_1 \cos \theta \hat{k}$ ....(ii)
From (i) and (ii)
$p E \sin \theta = \sqrt{3} pE \cos \theta$
$\tan \theta = \sqrt{3}$
$\theta = 60^{\circ}$
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Concepts Used:
Electric charges and field
What is Electric Charge
It is the property of subatomic particles that experiences a force when put in an electric and magnetic field.
What is Electric Field
It is a property associated with each point in space when charge is present in any form. The magnitude and direction of the electric field are expressed by E, called electric field strength or electric field intensity.
Electric charges are of two types: Positive and Negative. It is commonly carried by charge carriers protons and electrons.
Properties of Electric Charge
Various properties of charge include the following :-
- Additivity of Electric Charge
- Conservation of Electric Charge
- Quantization of Electric Charge
Types of electric charge
Two kinds of electric charges are there :-
Negative Charge - When an object has a negative charge it means that it has more electrons than protons.
Positive Charge - When an object has a positive charge it means that it has more protons than electrons.
When there is an identical number of positive and negative charges, the negative and positive charges would cancel out each other and the object would become neutral.