Q181 / 200 · MHT CET - Medical 2026 (22 April Shift 1) · Physics
An electric dipole is placed parallel to the electric field . Let 'W' be the work done in rotating the dipole by $60^\circ$ . Now, it is further rotated by $120^\circ$, the total work done is
$[\sin 30^\circ = \cos 60^\circ = 0.5,\ \cos 0^\circ = \sin 90^\circ = 1,\ \cos\pi^c = -1]$
$[\sin 30^\circ = \cos 60^\circ = 0.5,\ \cos 0^\circ = \sin 90^\circ = 1,\ \cos\pi^c = -1]$
- A$\text{W}/2$
- B$2\text{W}$
- C$3\text{W}$
- Correct answerD$4\text{W}$
Solution
The work done in rotating an electric dipole in a uniform electric field from an initial angle $\theta_1$ to a final angle $\theta_2$ is given by $W = pE(\cos\theta_1 - \cos\theta_2)$.
Initially, the dipole is parallel to the electric field, so $\theta_1 = 0^\circ$.
The work done in rotating the dipole by $60^\circ$ is:
$W = pE(\cos 0^\circ - \cos 60^\circ)$
$W = pE(1 - 0.5) = 0.5 pE$
$\Rightarrow pE = 2W$
The dipole is further rotated by $120^\circ$, making the final angle with the electric field $\theta_2 = 60^\circ + 120^\circ = 180^\circ$.
The total work done from the initial position is:
$W_{\text{total}} = pE(\cos 0^\circ - \cos 180^\circ)$
$W_{\text{total}} = pE(1 - (-1)) = 2pE$
Substituting $pE = 2W$:
$W_{\text{total}} = 2(2W) = 4W$
Answer: $4\text{W}$
Initially, the dipole is parallel to the electric field, so $\theta_1 = 0^\circ$.
The work done in rotating the dipole by $60^\circ$ is:
$W = pE(\cos 0^\circ - \cos 60^\circ)$
$W = pE(1 - 0.5) = 0.5 pE$
$\Rightarrow pE = 2W$
The dipole is further rotated by $120^\circ$, making the final angle with the electric field $\theta_2 = 60^\circ + 120^\circ = 180^\circ$.
The total work done from the initial position is:
$W_{\text{total}} = pE(\cos 0^\circ - \cos 180^\circ)$
$W_{\text{total}} = pE(1 - (-1)) = 2pE$
Substituting $pE = 2W$:
$W_{\text{total}} = 2(2W) = 4W$
Answer: $4\text{W}$
Hence, the correct answer is option: 'D'.