Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centers coincide. Find the magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.
nl = 100
ns = 50
rl = 10 cm
rs = 5 cm
Both the coils have a common center and hence the effect due to the current flowing will depend on the direction of flow. We can calculate the individual results and then do the vector addition of both the forces to get the resultant magnetic fields
1) In the same sense
Field due to larger coil
Field due to smaller coil
As the direction is same and both the fields are acting in the same direction, that outside the plane of the paper, we can simply perform a scalar addition
Similarly for
2) Opposite sense
As the direction is opposite, we can simply perform scalar subtraction to get the resultant
∴ 