Question

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

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

Answer 1

Answer: (B)

$\frac{5}{4} \mu_0$

Answer 2

Two coils carry currents in opposite directions, hence net magnetic field at center will be difference of the two fields. ie, $B_{net}=\frac{\mu_{0}}{4 \pi} \cdot 2 \pi N \frac{i_{1}}{r_{1}}-\frac{i_{2}}{r_{2}}$ $=\frac{10 \mu_{0}}{2} \frac{02}{02}-\frac{0.3}{0.4}$ $=\frac{5}{4} \mu_{0}$