Question

A. Derive the expression for electric field at a point on the equatorial line of an electric dipole.
B. Depict the orientation of the dipole in (i) stable, (ii) unstable equilibrium in a uniform electric field.

Answer 1

Derivation of the expression for electric field at a point on the equatorial line of an electric dipole.

• Enet = 2Ecos(theta)

• Enet = 2[ Kq / {√(r^2 + (a/2)^2)}^2 ]×(a/2)/√[r^2 + (a/2)^2]

= Kqa / { r^2 + (a/2)^2 }^3/2

• If r >> a then Enet = KP/r^3

• As the direction of E at equatorial positon is opposite of P so we can write in vector form :

• Eeqt = - KP/r^3

=> Orientation of the dipole in uniform electric field

• In this case, Fnet = 0, Net torque = 0

• We know that,

Net torque = q×E = qEsin(theta)

(i) stable

• Dipole is place along electric field.

• Theta = 0, there is minimum P.E

(ii) unstable

• Dipole is place opposite to the direction of electric field.

• Theta = 180°C, there is maximum of P.E