33. Fine electric field vector E at point P in terms of i,j.(the dipole p is very small

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Q. Statement I: The electric field due to a very small dipole at a large distance from its centre along its axis is

\frac{2 \to P}{4 π ε_{0} r^{3}} .

Statement II: Coulomb’s inverse square law is not valid in case of electric field due to a dipole.

An electric dipole of momentum $\to p$ is placed in a uniform electric field. The dipole is rotated through a very small angle from equilibrium and is released. Prove that it executes simple harmonic motion with frequency $f = \frac{1}{2 π} \sqrt{\frac{p E}{I}}$ . Where, $I =$ moment of inertia of the dipole.

Q. An electric dipole of momentum

\to p

is placed in a uniform electric field. The dipole is rotated through a very small angle

θ

from equilibrium and is released, find the time period of simple harmonic motion.

Q. A small electric dipole is placed at origin with its dipole moment directed along positive x - axis. The direction of electric field at point

(2, 2 \sqrt{2}, 0)

Q. Assertion :On going away from a point charge or a small electric dipole, electric field decreases at the same rate in both the cases. Reason: Electric field is inversely proportional to square of distance from the charge or on electric dipole.

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