An electric dipole, made up of positive and negative charges, each of 1 μC and placed at a dista

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An electric dipole, made up of positive and negative...

An electric dipole, made up of positive and negative charges, each of $1 \mu \mathrm{C}$ and placed at a distance $2 \mathrm{~cm}$ apart. If the dipole is placed in an electric field of $10^{5} \mathrm{~N} / \mathrm{C}$ then the maximum torque which the field can exert on the dipole, if it is turned from a position $\theta=0^{c}$ to $\theta=180^{\circ}$ is, is : (a) $2 \times 10^{-3} \mathrm{~N}-\mathrm{m}$ (b) $3 \times 10^{-3} \mathrm{~N}-\mathrm{m}$ (c) $4 \times 10^{-3} \mathrm{~N}-\mathrm{m}$ (d) $2.8 \times 10^{-3} \mathrm{~N}-\mathrm{m}$

An electric dipole, made up of positive and negative charges, each of $1 \mu \mathrm{C}$ and placed at a distance $2 \mathrm{~cm}$ apart. If the dipole is placed in an electric field of $10^{5} \mathrm{~N} / \mathrm{C}$ then the maximum torque which the field can exert on the dipole, if it is turned from a position $\theta=0^{c}$ to $\theta=180^{\circ}$ is, is :
(a) $2 \times 10^{-3} \mathrm{~N}-\mathrm{m}$
(b) $3 \times 10^{-3} \mathrm{~N}-\mathrm{m}$
(c) $4 \times 10^{-3} \mathrm{~N}-\mathrm{m}$
(d) $2.8 \times 10^{-3} \mathrm{~N}-\mathrm{m}$

Key Concepts

Electric Dipole

An electric dipole consists of two equal and opposite point charges separated by a small distance. It is a fundamental concept in electromagnetism, characterizing the simplest nontrivial charge distribution and playing a key role in interactions with electric fields.

Dipole Moment

The dipole moment is a vector quantity defined as the product of one of the charges and the separation distance between them. It quantifies the strength and orientation of the dipole, serving as a measure of the dipole's ability to interact with external electric fields.

Electric Field

The electric field is a vector field that represents the force per unit positive charge at any point in space. It is pivotal in understanding how charge distributions interact and how dipoles experience forces and torques when placed in it.

Torque on a Dipole

When an electric dipole is placed in an electric field, it experiences a torque that tends to align the dipole with the field. This torque is given by the cross product of the dipole moment and the electric field, highlighting how the orientation of the dipole relative to the field affects the rotational force.

Angular Dependence of Torque

The torque on a dipole in an electric field depends on the sine of the angle between the dipole moment and the electric field direction. This angular dependence means that maximum torque occurs when the dipole is perpendicular to the field, which is a key concept in analyzing the rotational behavior of dipoles in external fields.

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