Question

What is the net interaction force between two opposite charges in a uniform electric field, when (1) the dipole is aligned along the electric field direction, and (2) when it is not?

Answer 1

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_"+q "= qE`

`F_"-q" = -qE`

`F_"net"= F_"+q " + F_"-q" = qE -qE =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 `= rF = 0*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_"net"= F_"+q " + F_"-q" = qE -qE =0`

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

Torque `= rFsintheta = d(qE)sintheta = qdEsintheta = pE sintheta`
or
`vec tau = vec p xx vec E`

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