Question

Two concentric circular coils A and B have radii $25cm$ and $15cm$ and carry currents $10A$ and $15A$ respectively. A has $24$ turns and $B$ has $18$ turns. The direction of currents are in opposite order. The magnetic induction at the common centre of the coil is:

• A. $120{\mu }_{0}T$
• B. $480{\mu }_{0}T$
• C. $420{\mu }_{0}T$
• D. ${\mu }_0$

Answer 1

The correct option is C $420{\mu }_{0}T$

$B_1=\frac{n_1{\mu }_0{i}_1}{2r_1}$
$=\frac{24\times {\mu }_0\times 10}{2\times 25\times {10}^{-2}}$

$=480{\mu }_{0}T$ going into the plane
$B_2=\frac{n_2{\mu }_0{i}_2}{2r_2}$
$=\frac{18\times {\mu }_0\times 15}{2\times 15\times {10}^{-2}}$

$=900{\mu }_{0}T$ going out of the plane
$Bnet=B_2-B_1$
$=(900-480){\mu }_0$
$=420{\mu }_{0}T$