Question

Figure shows a coil of radius $2cm$ concentric with a coil of radius $7cm$ Each coil has $1000$ turns with a current of $5A$. In larger coil, then the current needed in the smaller coil to give the total magnetic field at the centre equal to $2mT$ is :

• A. $1.49A$
• B. $1.84A$
• C. $2.88A$
• D. $3.4A$

Answer 1

The correct option is A $1.49A$

magnetic field due to larger coil =$\frac{N{\mu }_{0}i}{2r}$
=$\frac{1000\times {\mu }_0\times 5\times T}{2\times 7\times {10}^{-2}}$( into the plane)
$=44.88mT$
magnetic field due to smaller coil =$\frac{N{\mu }_{0}i}{2r}$
=$\frac{1000\times {\mu }_0\times I\times T}{2\times 2\times {10}^{-2}}$ (out of the plane)
$=44.88mT$
${\left|B\right|}_{net}=\left(44.88\right)-\left(31.4\right)I$
$\therefore I=1.49A$