Question

Two coplanar concentric circular coils of radii $r$ and $\text{2} \, r$ , have the same number of turns $n$ . The smaller coil carries a clockwise current $i$ , while the larger coil carries an anticlockwise current $\text{2} \, i$ . The magnetic field induction at the centre is

• A. $\frac{3 \mu _{0} n i}{4 r}$
• B. zero
• C. $\frac{\mu _{0} n i}{4 r}$
• D. $\frac{\mu _{0} n i}{2 r}$

Answer 1

Answer: (B)

$B_1=\frac{\mu_0 n i}{2 r}, B_2=\frac{\mu_0 n(2 i)}{2(2 r)}$
$B_{R}=B_{1}-B_{2}$
$B_{1}=B_{2}$, both are in opposite direction