Question

What is meant by magnetic effect of electric current? Find the expression for the force acting between two parallel current-carrying conducting wires. On this basis, define the unit of electric current 'ampere'.

Hint:

The magnetic force between two parallel current-carrying wires is proportional to the product of the currents and inversely proportional to the distance between the wires. The definition of the ampere is based on the force between two conductors carrying a constant current.

Answer 1

The magnetic effect of electric current refers to the magnetic field produced by an electric current. When a current flows through a conductor, it creates a magnetic field around the conductor. This magnetic field can interact with other currents and produce forces. This effect is the basis of electromagnetism.
The force between two parallel current-carrying wires can be derived using Ampère's force law. The magnetic force per unit length between two parallel wires carrying currents \(I_1\) and \(I_2\) is given by the formula:
\[ F/L = \frac{\mu_0 I_1 I_2}{2 \pi r} \] Where: - \(F\) is the force between the wires,
- \(L\) is the length of the wire,
- \(r\) is the distance between the wires,
- \(\mu_0\) is the permeability of free space (\(\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}\)),
- \(I_1\) and \(I_2\) are the currents in the wires.
This force is attractive if the currents are in the same direction and repulsive if the currents are in opposite directions.
Now, the unit of electric current, the ampere, is defined based on this magnetic force. The definition is as follows:
"An ampere is the constant current which, if maintained in two straight parallel conductors of infinite length, of negligible cross-section, and placed 1 meter apart in vacuum, would produce a force of \(2 \times 10^{-7}\) newtons per meter of length." This definition links the electric current to the magnetic force between conductors.