Two coils P and Q of radius R and 2R are lying in the same plane with their centres coinciding. Find the magnitude and direction of the resultant magnetic field at the common centre if they respectively carry currents 3I and 2I in opposite directions.

Given
the radius of coil P = R
the radius of coil Q = 2R
Are both coils are lying in the same plane and their centres are coinciding

The magnetic field at the centre of the coil is
$B= \frac{\mu _{0}I}{2R}$
magnetic field due to coil P of carrying current 3I
$B_{p}= \frac{\mu _{0}\times 3I}{2R}= \frac{3\mu _{0}I}{2R}$
magnetic field due to coil Q of carrying current 2I
$B_{q}= \frac{\mu _{0}\times 2I}{2\times 2R}= \frac{\mu _{0}I}{2R}$
As the director of the current is opposite the magnetic field are also opposite

$B_{r}= \frac{3\mu _{0}I }{ 2R}-\frac{\mu _{0}I}{2R}= \frac{2\mu _{0}I }{ 2R}= \frac{\mu _{0}I}{R}$
Th resultant direction of the magnetic field is in the direction of the magnetic field produced by coil P.

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