Question #c26e2

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Jan 20, 2018

Zero. But ...
the torque associated with the electric forces not be zero.

Explanation:

A dipole is composed of two opposite charges + q and -q separated by a distance d. The product p=qd is called dipole moment.

When the dipole is exposed to electric field, each charge experiences a force. They are equal and opposite to each other. Hence the resultant force is zero . However together as a dipole, they do experience a torque.

(1) When the dipole is aligned with the electric field.
The forces acting on the two charges are:

${F}_{\text{+q }} = q E$

${F}_{\text{-q}} = - q E$

${F}_{\text{net"= F_"+q " + F_"-q}} = q E - q E = 0$

In the case, the two forces are directly opposing each other on the same line, hence no torque is exerted on the dipole.

Torque $= r F = 0 \cdot F = 0$

(2) The dipole is not aligned with the electric field and makes angle $\theta$ with the electric field.

Again, the forces acting on the charges are

${F}_{\text{net"= F_"+q " + F_"-q}} = q E - q E = 0$

However, this two forces are not on the same line, a torque is ensured. The magnitude of the torque is:

Torque $= r F \sin \theta = d \left(q E\right) \sin \theta = q \mathrm{dE} \sin \theta = p E \sin \theta$
or
$\vec{\tau} = \vec{p} \times \vec{E}$

The torque causes the dipole to oscillate in the electric field.

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