its easy

Electricity and Magnetism Level pending

Two circular coils radii 10cm and 40cm are connected in series to a battery. The ratio of magnetic fields at the centre of first coil to that of second coil is

2 : 1 4 : 1 1 : 2 1 : 4

Divyansh Tripathi by divyansh tripathi , 21, India

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1 solution

Caleb Townsend
Feb 24, 2015

The magnetic field at the center of a coil is B = μ 0 I 2 R B = \frac{\mu_0 I}{2R} So knowing that R 2 = 4 R 1 , R_2 = 4R_1, it is an easily solved ratio. B 1 B 2 = ( μ 0 I 2 R 1 ) ( μ 0 I 8 R 1 ) = 8 2 = 4 \frac{B_1}{B_2} = \frac{(\frac{\mu_0 I}{2R_1})}{(\frac{\mu_0 I}{8R_1})} = \frac{8}{2} = \boxed{4}

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