Answer :

(a) The torque acting on the dipole is given by,

Where, F= Magnitude of force

r= perpendicular distance.

This is vector notation of torque.

(b) The net force becomes zero when the dipole is place in non - uniform electric field.

(c) (i) For parallel p, θ=0

Thus, sin θ=0

The torque acting on the dipole is given by,

τ = pE sin θ = 0

Thus, torque becomes zero when p is parallel.

(ii) For perpendicular p, θ = 90

Thus, sin θ = 1

The torque acting on the dipole is given by,

τ= pE sin θ = pE

Thus, torque increases when p is perpendicular.

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