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.