Two long thin parallel wires are placed at a distance (r) from each other carrying equal current I  in opposite direction. The magnitude of force per unit length which is exerted by each wire on the other is :

CONCEPT:

Magnetic field:

• The space or region around the current-carrying wire/moving electric charge or around the magnetic material in which force of magnetism can be experienced by other magnetic material is called as magnetic field/magnetic induction by that material/current.
• It is denoted by B.
• The magnetic force per unit length between two parallel wires is given by;

\(\frac{F}{l} = \frac{{{\mu _o}}}{{2\pi }}\frac{{2{I_1}{I_2}}}{d}\)

Where μ0 = permittivity of free space, I1 = current in a first wire, I2 = current in a second wire,d = distance between two wires, and l = length of current-carrying wire.

EXPLANATION:

​Given - I₁ = I₂ = I and distance the between the two-wire (d) = r

• The magnetic force per unit length between two parallel wires is given by;

\(\Rightarrow \frac{F}{l} = \frac{{{\mu _o}}}{{4\pi }}\frac{{2{I_1}{I_2}}}{d}\)

\(\Rightarrow \frac{F}{l} = \frac{{{\mu _o}}}{{4\pi }}\frac{{2{I^2}{}}}{r}=\frac{\mu_o}{2\pi}\frac{I^2}{r}\)

• As the current in the wire is in the opposite direction, then the force between them will be repulsive.

Important Points

• If the conductor carries the current in the same direction, then the force between them will be attractive.
• If the conductor carries the current in the opposite direction, then the force between them will be repulsive