Question

What is the source of force acting on a current-carrying conductor placed in a magnetic field? Obtain the expression for the force acting between two long straight parallel conductors carrying steady currents and hence define Ampère’s law.

Hint:

The force between two parallel conductors carrying current is inversely proportional to the distance between them.

Answer 1

The source of the force acting on a current-carrying conductor placed in a magnetic field is the magnetic interaction between the moving charges (current) in the conductor and the external magnetic field. The force on a current-carrying conductor in a magnetic field is given by: \[ F = I L B \sin(\theta) \] Where:
\( F \) is the force,
\( I \) is the current,
\( L \) is the length of the conductor in the magnetic field,
\( B \) is the magnetic field strength,
\( \theta \) is the angle between the magnetic field and the conductor.

For two long, straight, parallel conductors carrying steady currents \( I_1 \) and \( I_2 \), the force per unit length between them is given by Ampère's law: \[ F = \frac{\mu_0 I_1 I_2}{2 \pi d} \] Where: 
\( \mu_0 \) is the permeability of free space, 
\( d \) is the distance between the two conductors.

This is the expression for the force between two parallel conductors carrying steady currents, and it defines Ampère's law.