Q92 / 180 · AIIMS 2014 · Physics

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

  • A
    $1$
  • Correct answer
    B
    $2$
  • C
    $3$
  • D
    $4$

Solution

$\frac{\mu_0}{4 \pi} \frac{2 i_1}{r}-\frac{\mu_0}{4 \pi} \frac{2 i_2}{r}=10 \mu \mathrm{T}$ $\frac{\mu_0}{4 \pi} \frac{2 i_1}{r}+\frac{\mu_0}{4 \pi} \frac{2 i_2}{r}=30 \mu \mathrm{T}$ On solving $i_1=20 \mathrm{~A}$ and $i_2=10 \mathrm{~A} . \therefore i_1 / i_2=2$

Hence, the correct answer is option: 'B'.

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