First slide

Magnetic field due to current element

Question

Currents $I_{1}$ and $I_{2}$ 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

$M a g n e t i c f i e l d d u e t o b o t h w i r e s w i l l b e e q u a l a n d o p p o s i t e i n d i r e t i o n \frac{μ_{0} I_{1}}{4 π (a + x)} = \frac{μ_{0} I_{2}}{4 π (a - x)} \Leftrightarrow \frac{a - x}{a + x} = \frac{I_{2}}{I_{1}} \Rightarrow x = (\frac{I_{1} - I_{2}}{I_{1} + I_{2}}) a .$

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