Consider the following statements about electric dipole and select the correct ones.
`S_(1)`: Electric dipole moment vector `vec(p)` is directed from the negative charge to the positive charge
`S_(2)`: The electric field of a dipole potential falls off as `(1)/(r^(2))` and not as `(1)/(r )`
`S_(3)`: The electric field of a dipole at a point with position vector `vec(r )` depends on `|vec(r )|` as well as s angle between `vec(r ) and vec(p)`
`S_(4)`: In a uniform electric field, the electric dipole experience no net force but a torque

Options

A. S2, S3 and S4
B. S3 and S4
C. S2 and S3
D. all four

Answer

D

Explanation

An electric dipole is a pair of equal and opposite charges q and -q separated by some distance 2a. Its dipole moment vector `vec(p)` has magnitude 2qa and is in the direction of the dipole axis from -q to q.

The electric field due to a dipole at a pioint P is
`(Q_(1))/(4pi R^(2)) = (Q_(1) + Q_(2))/(4pi)(4R^(2))E = (p)/(4pi epsilon_(0))(sqrt(3 cos^(2) theta + 1))/(r^(3)) (r gt gt a)`
The electric dipole potential falls off at large distance, as `(1)/(r^(2))` not as `(1)/(r )`, characteristic of the potential due to single charge. In a uniform electric field `vec(E)`, a dipole experiences a torque `vec(tau)` given by `vec(tau) = vec(p) xx vec(E)` but experiences no net force.) `= (Q_(1) + Q_(2) + Q_(3))/(4pi (9R^(2)))`