Two circular coils of radii 5cm and 10cm carry currents of 2A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as their centres coincide. Magnitude of magnetic field at the common centre of coils is

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8 $π \times$ 10^–4 T if currents in the coils are in same sense

8 $π \times$ 10^-4 T if currents in the coils are in opposite sense

4 $π \times$ 10^–4T if currents in the coils are in opposite sense

zero if currents in the coils are in opposite sense

answer is A, C.

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Detailed Solution

$B_{1} = \frac{μ_{0} N_{1} i_{1}}{2 R_{1}}$

$= \frac{(4 π \times 10^{- 7}) (50) (2)}{2 (5 \times 10^{- 2})} = 4 π \times 10^{- 6} T$

$B_{2} = \frac{μ_{2} N_{2} i_{2}}{2 R_{2}} = \frac{(4 π \times 10^{- 7}) (100) (2)}{(2) (10 \times 10^{- 2})}$

$= 4 π \times 10^{- 4} T$

When currents are in the same direction B_net = B₁+B₂.

When currents are in the opposite direction B_net = B₁–B₂

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