Q155 / 160 · AP EAMCET 2008 · Physics

Two concentric coils of 10 turns each are placed in the same plane. Their radii are $20 \mathrm{~cm}$ and $40 \mathrm{~cm}$ and carry 0.2 and $0.3 \mathrm{~A}$. current respectively in opposite directions. The magnetic induction (in T) at the centre is

  • A
    $\frac{3}{4} \mu_0$
  • Correct answer
    B
    $\frac{5}{4} \mu_0$
  • C
    $\frac{7}{4} \mu_0$
  • D
    $\frac{9}{4} \mu_0$

Solution

Two coils carry currents in opposite directions, hence net magnetic field at centre will be difference of the two fields. ie, $$ \begin{aligned} B_{\text {net }} & =\frac{\mu_0}{4 \pi} \cdot 2 \pi N\left[\frac{i_1}{r_1}-\frac{i_2}{r_2}\right] \\ & =\frac{10 \mu_0}{2}\left[\frac{0.2}{0.2}-\frac{0.3}{0.4}\right] \\ & =\frac{5}{4} \mu_0 \end{aligned} $$

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

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