An electric dipole is placed at the centre of a sphere. Which of the following is correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → The electric field is non-zero at every point on the sphere.
A dipole is a pair of equal and opposite charges \( +q \) and \( -q \). The field at any point is the vector sum of the fields of the two charges. The flux through a closed surface depends only on the net charge enclosed.
Option (1) The electric field is zero everywhere on the sphere. — Incorrect. Only the total flux through the sphere is zero. The field itself falls off with distance but does not vanish at the points of the sphere.
Option (2) The electric flux through the sphere is non-zero. — Incorrect. By Gauss’s law the flux is \( q_{\mathrm{enclosed}}/\varepsilon_0 \). The sphere encloses \( +q \) and \( -q \), so the net charge inside is zero and the flux is zero.
Option (3) The electric field is zero at some points on the sphere. — Incorrect. The two fields add to zero only where they are equal in size and opposite in direction.
On the dipole axis the point is nearer one charge, so the two fields differ in size.
At every other point, the lines joining it to \( +q \) and \( -q \) are not along one line. So the two fields cannot be opposite.
Option (4) The electric field is non-zero at every point on the sphere. — Correct. The fields of \( +q \) and \( -q \) never add to zero at any point of the sphere. So the resultant field is present everywhere on it. For a dipole of moment \( p \), at large \( r \) the field is \( 2kp/r^{3} \) on the axis and \( kp/r^{3} \) on the equatorial plane, with \( k=1/4\pi\varepsilon_0 \).