An electric dipole of moment $\vec{p}$ is lying along a uniform electric field $\vec{E}$. The work done in rot

Question

An electric dipole of moment $\vec{p}$ is lying along a uniform electric field $\vec{E}$. The work done in rotating the dipole by $90^{\circ}$ is:

Accepted Answer

The work done by an external agent in rotating an electric dipole from an initial angle $	heta_0$ to a final angle $	heta_1$ in a uniform electric field is given by the change in potential energy: $W = U_{	heta_1} - U_{	heta_0} = pE(\cos	heta_0 - \cos	heta_1)$ [NCERT Class 12, Physics Part I, Sec 2.8.3, Eq 2.31].

1.  **Initial Position:** The dipole is lying along the electric field, which corresponds to the position of stable equilibrium. Thus, $	heta_0 = 0^{\circ}$.
2.  **Final Position:** The dipole is rotated by $90^{\circ}$. Thus, $	heta_1 = 90^{\circ}$.
3.  **Calculation:**
    $$W = pE(\cos 0^{\circ} - \cos 90^{\circ})$$
    $$W = pE(1 - 0)$$
    $$W = pE$$

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