Two parallel long current carrying wire separated by a distance 2 r are shown in the figure. The ratio of magnetic field at A to the magnetic field produced at C is x/7. The value of x is __________.

Solution

Physics sir · 4 steps

Both currents point the same way, so outside the pair the two fields add. Just get each distance right.

1. Field of each wire. A long straight wire gives B = (μ₀ I)/(2π d) at distance d. Both currents, I and 2I, flow in the same direction. At any point outside the pair, on one side of both wires, the two fields point the same way and add.
2. Distances at A. A is r from the wire carrying I. It is r + 2r = 3r from the wire carrying 2I. So B_A = μ₀/2π(I/r + 2I/3r) = μ₀/2π·5I/3r.
3. Distances at C. C is r from the wire carrying 2I and 3r from the wire carrying I. So B_C = μ₀/2π(2I/r + I/3r) = μ₀/2π·7I/3r.

   B_A/B_C = (5I/3r)/(7I/3r) = 5/7

4. So. The ratio is 5/7, so x = 5.

The common slip: 5.6. Taking the far wire at distance 2r instead of 3r gives B_A/B_C = 4/5, so x = 5.6, not 5.

The idea to keep. For two parallel wires with currents in the same direction, the fields add outside the pair and oppose between them. Measure each distance from its own wire.

Answer from the NTA final answer key. Solution by PrepWiser.