A short electric dipole of dipole moment is placed at a distance r from the centre of a solid metallic sphere of radius a (<< r) as shown in the figure. The electric field intensity at the centre of sphere C due to induced charge on the sphere is

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$\frac{1}{4 π ε_{0}} \frac{2 p}{r^{3}}$ along CO

$\frac{1}{4 π ε_{0}} \frac{2 p}{r^{3}}$ along OC

zero

$\frac{1}{4 π ε_{0}} \frac{p}{r^{3}}$ along CO

answer is B.

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Detailed Solution

Electric field at C due to electric dipole $= \frac{1}{4 π ε_{0}} \frac{2 p}{r^{3}}$ along OC

Electric field at C due to induced charge must be equal and opposite to electric field due to dipole as net field at C is zero.

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