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 centres 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.

Explanation

To find the magnitude of the magnetic field \( B \) at the common center of two circular coils carrying equal currents, we will analyze the two scenarios: (a) when the currents are in the same direction and (b) when the currents are in opposite directions.

### Given Data:
- Radius of Coil 1, \( R_1 = 5 \) cm = \( 5 \times 10^{-2} \) m
- Radius of Coil 2, \( R_2 = 10 \) cm = \( 10 \times 10^{-2} \) m
- Current in both coils, \( I_1 = I_2 = 2 \) A
- Number of turns in Coil 1, \( N_1 = 50 \)
- Number of turns in Coil 2, \( N_2 = 100 \)
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