Question

When an electric dipole $\vec{p}$ is placed in a uniform electric field $\vec{E}$ then at what angle between $\vec{P}$ and $\vec{E}$ the value of torque be maximum?

Answer 1

Hint: As we know torque is used to define a force applied to an object in the given question the force is applied in the form of the electric field. So, on placing the dipole in the electric field, the direction will be clockwise if it is positive, and the direction will be anticlockwise if it is negative. Use this concept to solve the problem.






Formula used:
$ \tau=\vec{p}\times\vec{E}\ sin\theta$
Where; τ = torque
$\vec{p}$ = magnitude of the charges on both the ends/point of the dipole
$\vec{E}$ = Electric field applied on the dipole
ϴ = Angle of rotation of dipole with its axis in presence of electric field








Complete answer:
On both the dipoles, the force will be
$\tau=+q\times\vec{E}\ sin\theta$ (anticlockwise for the one point of the dipole)
$\tau=-q\times\vec{E}\ sin\theta$ (clockwise for the other point of the dipole)
So, the torque acting on the dipole is
$\tau=q\times\vec{E}\ sin\theta$
Since; Since the values of sinϴ are-
As, Sin90˚= 1
So we can see that at an angle of 90˚ the dipole will experience the maximum torque because its value is 1 (maximum).
Thus, the value of torque will be maximum at an angle of 90˚






Note: Torque is a vector quantity it depends on the direction of the force. The distance between the point where force is applied and the point of rotation at the dipole is called an arm. One should know the concept of stable and unstable equilibrium also to understand the question.