In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 10⁵ NC^–1 per metre. What are the force and torque experienced by a system having a total dipole moment equal to 10^–7 cm in the negative z-direction?

Solution

Force is acting on an electric dipole in the positive z-direction which is placed in a non-uniform electric field.

As, the electric field changes uniformly in the positive z-direction only.
Thus,

As, the system has the total dipole moment equal to 10^–7 Cm in the negative z-direction. Thus,

It is indicated by the negative sign that the force 10^–2 N acts in the negative z-direction.

In an electric field

\vec{E},

the torque on dipole moment

\vec{P}

is given by

\vec{τ} = \vec{p} \times \vec{E}

|\vec{τ}| = pE \sin θ

\vec{P} and \vec{E}

are acting in opposite direction,

θ = 180 °,

∴

|\vec{t}| = pE \sin 180 ° = 0 .

Hence, the torque experienced by the system is 0.

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