Question

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

• A. $\frac{3{\mu }_{o}ni}{4r}$
• B. zero
• C. $\frac{{\mu }_{o}ni}{4r}$
• D. $\frac{{\mu }_{o}ni}{2r}$

Answer 1

The correct option is B zero

B due to Bigger radius coil $=\frac{{\mu }_0\left(2i\right)}{2\cdot \left(2r\right)}$ going out of the plane
$=\frac{{\mu }_{0}i}{2r}$
B due to smaller radius coil $=\frac{{\mu }_{0}i}{2r}$ going into the plane
So $B_{net}=0$