Question

An electric dipole is placed in an electric field generated by a point charge.
A. The net electric force on the dipole must be zero
B. The net electric force on the dipole may be zero.
C. The torque on the dipole due to the field must be zero.
D. The torque on the dipole due to the field may be zero.

Answer 1

Hint:As we know, the same charges repel each other and opposite charges attract each other. As we know that for a positive charge( +q) the direction of the electric force is in the direction of the electric field and for a negative charge (–q) the direction of the electric force is in the opposite direction of the electric field.

Formula used:
Force on the dipole is given as,
\[F = (p \cdot \nabla )E\]
Where p is the dipole moment and E is the electric field.
Torque is given by,
\[\tau = \overrightarrow p \times \overrightarrow E \]

Complete step by step solution:
As the electric field is non-uniform. So the magnitude of forces is not equal as it depends on the strength of the electric field. Therefore net force is not equal to zero. Force on the dipole is:
\[F = (p \cdot \nabla )E\]
Here the electric field is not always equal to zero i.e. \[E \ne 0\]
As torque is given by,
\[\tau = \overrightarrow p \times \overrightarrow E = pE\sin \theta \]

If the dipole moment and electric field are parallel then \[\theta = {0^0}\]. Now we have,
\[\begin{array}{l}\tau = pE\sin \theta \\ \Rightarrow \tau {\rm{ = pEsin}}{{\rm{0}}^0}\\ \Rightarrow \tau {\rm{ = 0}}\end{array}\]
Here the torque is zero. Hence if the dipole moment and electric field are parallel to each other then the torque may be zero. Therefore we concluded that if an electric dipole is placed in an electric field generated by a point charge then the torque on the dipole due to the field may be zero.

Hence option D is the correct answer.

Note: The dipole moment is a vector quantity with a magnitude equal to the product of charge and the distance between them and a direction will be from the negative charge to the positive charge. The torque can be measured as the cross product of dipole moments and the force acting on the dipole.