Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

An electric dipole of moment $p$ is placed in an electric field of intensity $E$ . The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta=90^\circ$ , the torque and the potential energy of the dipole will respectively be:

$pE\sin\theta, -pE\cos\theta$

$pE\sin\theta, -2pE\cos\theta$

$pE\sin\theta, 2pE\cos\theta$

$pE\cos\theta, -pE\sin\theta$

Step-by-Step Solution

Torque ( $\tau$ ): When an electric dipole of moment $\mathbf{p}$ is placed in a uniform electric field $\mathbf{E}$ , it experiences a torque given by the vector product $\tau = \mathbf{p} \times \mathbf{E}$ . The magnitude of this torque is $\tau = pE\sin\theta$ [NCERT Class 12, Physics Part 1, Sec 1.11, Eq. 1.22].
Potential Energy ( $U$ ): The potential energy of the dipole is the work done in rotating the dipole from a reference position (where potential energy is zero) to the current position $\theta$ . The standard reference position is taken at $\theta_0 = 90^\circ$ (perpendicular to the field). The work done is $U = \int_{90^\circ}^{\theta} \tau d\theta = \int_{90^\circ}^{\theta} pE\sin\theta d\theta = -pE [\cos\theta]_{90^\circ}^{\theta} = -pE\cos\theta$ [NCERT Class 12, Physics Part 1, Sec 2.8.3, Eq. 2.32].

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