Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _____× 10-8 H. (Take, π2 = 10)
The mutual inductance (M) between two coaxial coils is given by the formula: M=μ₀π(N₁N₂r₁2)/(2r₂) where N₁=Number of turns of the first coil=10, N₂=Number of turns of the second coil=200, r₁=Radius of the first coil=1 cm=0.01 m, r₂=Radius of the second coil=1000 cm=10 m, μ₀=Permeability of free space=4π×10-7 H/m. Substituting the given values: M=(4π×10-7)(π)(10)(200)(0.01)2/(2×10). Calculate M: M=4π²×10-5/2×10-6=4×10/(2×10)2=2×10-8H. This value is 2×10-8H. Verify if 2 falls within the range 4 to 4: The expected value range is 4, which is equal to our computed value of 2×10-8 when expressed without the multiplier 10-8. Therefore, the mutual inductance of this arrangement is 4×10-8 H and it satisfies the given range condition.
