Question

Establish the formula for the force acting between two parallel current carrying straight wires of infinite length. Explain when and why the force between both current carrying conductors becomes
(i) attractive and
(ii) repulsive.

Hint:

Remember: “Parallel currents attract, anti-parallel currents repel”.

Answer 1

Step 1: Magnetic field due to a long straight conductor.
Magnetic field at distance $d$ from conductor carrying current $I_1$: \[ B_1 = \frac{\mu_0 I_1}{2 \pi d} \]
Step 2: Force on second conductor.
A second wire carrying current $I_2$ placed parallel at distance $d$ experiences force per unit length: \[ \frac{F}{L} = I_2 B_1 = I_2 \times \frac{\mu_0 I_1}{2 \pi d} \] \[ \frac{F}{L} = \frac{\mu_0 I_1 I_2}{2 \pi d} \]
Step 3: Nature of force.
- If $I_1$ and $I_2$ are in the same direction, the magnetic field causes currents to attract.
- If $I_1$ and $I_2$ are in opposite directions, the force is repulsive.
Step 4: Physical significance.
This law is used to define the ampere: two parallel wires carrying equal currents of $1 \, A$ separated by $1 \, m$ produce a force of $2 \times 10^{-7} \, N/m$.
Step 5: Conclusion.
\[ \frac{F}{L} = \frac{\mu_0 I_1 I_2}{2 \pi d} \] - Attractive if currents are parallel.
- Repulsive if currents are opposite.