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 centre 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

The correct option is B $\frac{5}{4}{\mu }_0$

At the center of a current carrying loop, magnetic induction is given as,

$B=\frac{{\mu }_{0}NI}{2R}$

Here, as we have two concentric loops with current in opposite directions, net magnet induction as the center is,

$B_{net}=\frac{{\mu }_0{N}_1{I}_1}{2R_1}-\frac{{\mu }_0{N}_2{I}_2}{2R_2}$

$⟹B_{net}=\frac{{\mu }_0\times 10\times 0.2}{2\times 0.2}-\frac{{\mu }_0\times 10\times 0.3}{2\times 0.4}=5{\mu }_0/4$

Option B is correct.