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  4. Two parallel long wires A and B carry currents i1 and i2 (< i1). When i1 and i2 are in the same direction, the magnetic field at a point mid way between the wires is 10 μ T. If i2 is reverse the field becomes 30 μ T. The ratio i1/i2 is

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Q. Two parallel long wires A and B carry currents $i_1$ and $i_2 (< i_1)$. When $i_1$ and $i_2$ are in the same direction, the magnetic field at a point mid way between the wires is $10 \,\mu\,T$. If $i_2$ is reverse the field becomes $30\, \mu T$. The ratio $i_1/i_2$ is

AIIMSAIIMS 2014Moving Charges and Magnetism

Solution:

$\frac{\mu_{0}}{4\pi} \frac{2i_{1}}{r}-\frac{\mu_{0}}{4\pi} \frac{2i_{2}}{r}=10 \mu T$
$\frac{\mu _{0}}{4\pi }\frac{2i_{1}}{r}+\frac{\mu _{0}}{4\pi } \frac{2i_{2}}{r}=30 \mu T$
On solving $i_{1} = 20 A and i_{2} = 10 A. ∴ i_{1}/i_{2} = 2$