Two concentric flat coils of radius r_1 = 2 cm and t_2 = 5 cm are lying in the s

Question

Two concentric flat coils of radius r_1 = 2 cm and t_2 = 5 cm are lying in the same plane Each coil has N = 100 turns. The current I_1 in the smaller coil is (2 + 0.1 N) A while the current I_2 in the larger coil is (5 + 0.1n) A Find the magnitude of the magnetic field in the center of the coils if (a) the currents in both coils flow in the same direction, and (b) the currents in both coils flow in the opposite directions At which radius n of the smaller coil and at which directions of currents (same or opposite) the magnetic field in the center of the coils could be zero?

Explanation / Answer

a) magnetic field = 100 * (2 * 3.14 * 10-7) * (3.1/0.02 + 6.1/0.05)

                           = 0.01739 T

b)    magnetic field = 100 * (2 * 3.14 * 10-7) * (3.1/0.02 - 6.1/0.05)

                             = 0.0020724 T

For magnetic field zero

=> 3.1/r1 = 6.1/0.05

=> r1   =   2.54 cm          (radius of smaller coil)

=>   Direction of current should be in opposite direction .

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