Question

write an expression for the moment of force about a given axis

Answer 1

T = fd
where T is Torque or moment of force
f is the force applied
d is the perpendicular distance of the line of action of force from the point of pivot

Answer 2

The moment of force is represented by formula $\boldsymbol{\tau}=\boldsymbol{p} \boldsymbol{E} \sin \boldsymbol{\theta}$

Explanation:

The moment of force is defined as the force applied on the body to rotate in for a particular angular direction. It is termed as torque.

Let us consider a rod having charges of equal magnitude and opposite sign at its ends. The length of the rod is considered as 2d as the charges are forming a dipole. So when the rod is placed in an electric field. The force acting on +q is F = qE and the force acting on –q is F = -qE.

The force acting on both the ends have same magnitude but the forces are acting in opposite directions. This creates a torque in the rod.

$\text{Torque} = \text{Force} \times \text{Perpendicular distance between the forces}$

$\text{Torque} =F \times 2 d \sin \theta$

$\Rightarrow \text { Torque }=q E \times 2 d \sin \theta$

Since, $2qd=p$

$\text{Torque} =E \times p \sin \theta$

Or

$\text{Torque}=p E \sin \theta$