Two infinitely long parallel wires carrys currents of 100A and 200A respectively and they repel each other with a force of 0.4N/m.what is the distance between the two wires ?

Question

Answer

Calculating the Distance between Two Parallel Wires

To determine the distance between the two infinitely long parallel wires carrying currents of 100A and 200A, we can use the formula for the force between two parallel current-carrying wires.

Force between Two Parallel Wires
The force per unit length between two parallel wires is given by the formula:
$$ F = \frac{{\mu_0 \cdot I_1 \cdot I_2}}{2\pi \cdot d} $$

where:
- $ F $ = force per unit length
- $ \mu_0 $ = permeability of free space (4π x 10^-7 N/A^2)
- $ I_1 $ and $ I_2 $ = currents in the wires
- $ d $ = distance between the wires

Given that the force per unit length is 0.4 N/m, the currents in the wires are 100A and 200A, respectively, and the permeability of free space is 4π x 10^-7 N/A^2, we can substitute these values into the formula and solve for the distance $ d $.

Solving for Distance
$$ 0.4 = \frac{{4\pi \times 10^{-7} \times 100 \times 200}}{2\pi \times d} $$
$$ d = \frac{{4\pi \times 10^{-7} \times 100 \times 200}}{0.4 \times 2\pi} $$
$$ d = \frac{{8 \times 10^{-5}}}{0.8} $$
$$ d = 0.0001 \, m $$

Therefore, the distance between the two parallel wires is 0.0001 meters or 0.1 mm.

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