An electric dipole is held at an angle ø in a uniform external electric field E. will there be any (I) net translatory force (II) tarqce acting on it ? Explain what happens to dipole on being released.

When an electric dipole is placed in a uniform external electric field, it experiences specific forces and torques that can significantly affect its behavior. Let's break down your question into two parts: the net translatory force and the torque acting on the dipole, and then we'll discuss what happens when the dipole is released.

Net Translatory Force on the Dipole

In a uniform electric field, the forces acting on the positive and negative charges of the dipole are equal in magnitude but opposite in direction. This means that the net translatory force on the dipole is zero. To understand this better, consider the following:

• The dipole consists of two equal and opposite charges, +q and -q, separated by a distance d.
• When placed in an electric field E, the positive charge experiences a force of +qE in the direction of the field, while the negative charge experiences a force of -qE in the opposite direction.
• Since these forces are equal and opposite, they cancel each other out, resulting in a net force of zero.

Torque Acting on the Dipole

While there is no net translatory force, the dipole does experience a torque when it is placed at an angle ø in the electric field. The torque (τ) can be calculated using the formula:

τ = p × E

Where:

• p is the dipole moment, defined as p = qd, where q is the charge and d is the separation distance.
• E is the magnitude of the electric field.

The torque tends to align the dipole with the electric field. The direction of the torque is given by the right-hand rule, and it acts to rotate the dipole towards the direction of the field. The amount of torque depends on the angle ø; the greater the angle, the larger the torque.

Behavior Upon Release

When the dipole is released, it will experience a torque that causes it to rotate. As it rotates, the torque will do work on the dipole, converting potential energy into kinetic energy. The dipole will continue to rotate until it aligns itself with the electric field, reaching a position where the torque is zero (i.e., when ø = 0 degrees).

In summary, while there is no net translatory force acting on the dipole in a uniform electric field, there is a torque that causes it to rotate. Upon release, the dipole will move towards alignment with the field, illustrating the dynamic interaction between electric fields and dipoles.