Question

An electric dipole of moment \(P\) is placed along the direction of electric field \(E\). The work done in deflecting the dipole through \(180^\circ\) is equal to

• A. \(PE\)
• B. \(+2PE\)
• C. \(-2PE\)
• D. Zero

Hint:

Potential energy of dipole: \[ U=-PE\cos\theta \] Stable equilibrium: \[ \theta=0^\circ \] Unstable equilibrium: \[ \theta=180^\circ \]

Answer 1

The Correct Option is B

Step 1: Write the potential energy formula for dipole.
Potential energy of an electric dipole in electric field is: \[ U=-PE\cos\theta \] where: \[ \theta=\text{angle between } \vec{P} \text{ and } \vec{E} \]

Step 2: Find initial potential energy.
Initially dipole is along the field: \[ \theta_i=0^\circ \] Thus: \[ U_i=-PE\cos0^\circ \] \[ U_i=-PE \]

Step 3: Find final potential energy.
After deflection through: \[ 180^\circ \] \[ \theta_f=180^\circ \] Thus: \[ U_f=-PE\cos180^\circ \] \[ U_f=+PE \]

Step 4: Calculate work done.
Work done: \[ W=U_f-U_i \] \[ W=PE-(-PE) \] \[ W=2PE \]

Step 5: Identify the correct option.
Therefore: \[ \boxed{W=+2PE} \] Hence, the correct answer is: \[ \boxed{\mathrm{(B)}} \]