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NEETPhysicsMagnetic Effects of Current

Two concentric, coplanar circular coils A and B have radii in the ratio R_A : R_B = 1 : 2 and number of turns in the ratio N_A : N_B = 2 : 1 . If the net magnetic field at their common centre is zero, what is the ratio of their magnetic moments M_A : M_B ?

Options

  1. A1 : 8
  2. B1 : 1
  3. C2 : 1
  4. D1 : 4

Correct answer

A. 1 : 8

Step-by-step solution

For the net magnetic field at the centre to be zero, the magnetic fields produced by the two coils must be equal in magnitude and opposite in direction. B_A = B_B ₀ N_A I_A 2 R_A = ₀ N_B I_B 2 R_B Rearranging for the ratio of currents: I_A I_B = ( N_B N_A ) ( R_A R_B ) Substituting the given ratios N_A/N_B = 2/1 and R_A/R_B = 1/2 : I_A I_B = ( 1 2 ) ( 1 2 ) = 1 4 The magnetic moment of a coil is given by M = N I A = N I R^2 . The ratio of their magnetic moments is: M_A M_B = ( N_A N_B ) ( I_A I_B ) ( R_A R_B )^2 M_

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