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?

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Jan 20, 2018


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


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#
# vec tau = vec p xx vec E#

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

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