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

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Zero if current in the coils are in opposite sense

$8 π \times 10^{- 4} T$ , if current in the coils are in same sense

$4 π \times 10^{- 4} T$ , if current in the coils are in opposite sense.

$8 π \times 10^{- 4} T$ , if current in the coils is in opposite sense.

answer is A, C.

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Detailed Solution

Using $B = \frac{μ_{0} N i}{2 R}$
$B_{1} = B_{2} = 4 π \times 10^{- 4} T$
(i) If current in same sense $B_{n e t} = 8 π \times 10^{- 4} T$
(ii) If current in opposite sense, $B_{n e t} = 0$

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