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A positively charged very large sheet has a charge density of $' σ' coul / m^{2} .$ An electric dipole of moment ‘P’ is placed near the sheet of charge at right angles to the sheet as shown in figure. Find the work done in rotating the dipole through an angle of $180^{0} .$

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$\frac{σP}{2 ε_{0}}$

$\frac{2 σP}{ε_{0}}$

$\frac{σP}{ε_{0}}$

$\frac{\sqrt{2} σP}{ε_{0}}$

answer is D.

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Detailed Solution

$E = \frac{σ}{2 ε_{0}}, U_{i} = - \vec{P} . \vec{E} = - \frac{σρ}{2 ε_{0}}, U_{f} = - (- \vec{P}) . \vec{E} = + \frac{σP}{2 ε_{0}} ∴ W = U_{f} - U_{i} = \frac{σP}{ε_{0}}$

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