An electric dipole of moment $p$ is placed in an electric field of intensity $E$. The dipole acquires a positi

Question

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 $	heta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $	heta=90^\circ$, the torque and the potential energy of the dipole will respectively be:

Accepted Answer

1. **Torque ($	au$):** 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 $	au = \mathbf{p} 	imes \mathbf{E}$. The magnitude of this torque is $	au = pE\sin	heta$ [NCERT Class 12, Physics Part 1, Sec 1.11, Eq. 1.22].
2. **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 $	heta$. The standard reference position is taken at $	heta_0 = 90^\circ$ (perpendicular to the field). The work done is $U = \int_{90^\circ}^{	heta} 	au d	heta = \int_{90^\circ}^{	heta} pE\sin	heta d	heta = -pE [\cos	heta]_{90^\circ}^{	heta} = -pE\cos	heta$ [NCERT Class 12, Physics Part 1, Sec 2.8.3, Eq. 2.32].

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