First slide

Magnetic field due to a straight current carrying wire

Question

Current I₁ and I₂ flow in the wires shown in figure. The field is zero at distance x to the right of O. Then

Moderate

A

$x = (\frac{I_{1}}{I_{2}}) a$
B

$x = (\frac{I_{2}}{I_{1}}) a$
C

$x = (\frac{I_{1} - I_{2}}{I_{1} + I_{2}}) a$
D

$x = (\frac{I_{1} + I_{2}}{I_{1} - I_{2}}) a$

Solution

$\begin{array}{l} \frac{μ_{0} I_{1}}{4 π (a + x)} = \frac{μ_{0} I_{2}}{4 π (a - x)} \\ \frac{a - x}{a + x} = \frac{I_{2}}{I_{1}} \\ I_{1} a - I_{1} x = I_{2} a + I_{2} x \\ x = (\frac{I_{1} - I_{2}}{I_{1} + I_{2}}) a \end{array}$

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