An electric dipole having dipole moment ( 4 × 1 0 − 9 ) C − m is placed at origin along x-axis. What uniform electric field (in N/C) should be applied along x-axis so that we get a equipotential spher

Question

An electric dipole having dipole moment ( 4 × 1 0 − 9 ) C − m is placed at origin along x-axis. What uniform electric field (in N/C) should be applied along x-axis so that we get a equipotential spherical surface of radius 3m centred at origin ?

TestHub · Accepted Answer

For a spherical equipotential the net field on it must be purely radial, so the applied field cancels the dipole's tangential component.

$E sin θ = \frac{k P s i n θ}{R ^{3}}$ ⇒ $E = \frac{k P}{R ^{3}}$ .

$E = \frac{9 \times 1 0 ^{9} \times 4 \times 1 0 ^{- 9}}{27} = 1.33$ N/C

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