First slide

Magnetic field due to a straight current carrying wire

Question

Two parallel, long wires carry currents i₁ and i₂ with i₁ > i₂ . When the current are in the same direction, the magnetic field at a point midway between the wire is 10 mT. If the direction of i₂ is reversed, the field becomes 30 mT. The ratio i₁/i₂ is

Moderate

A

4
B

3
C

2
D

1

Solution

$\begin{array}{l} 10 mT = \frac{μ_{0}}{2 π (r / 2)} (i_{1} - i_{2}) \\ 30 mT = \frac{μ_{0}}{2 π (r / 2)} (i_{1} + i_{2}) \\ Dividing : i_{1} / i_{2} = 2 \end{array}$

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