Physics · Biot Savart law and its application to the current carrying circular loop
The electric current in a circular coil of two turns produced a magnetic inducti
The electric current in a circular coil of two turns produced a magnetic induction of \( 0.2 \mathrm{T} \) at its centre. The coil is unwound and then rewound into a circular coil of four turns. If same current flows in the coil, the magnetic induction at the centre of the coil now is:
- A. \( 0.2 T \)
- B. \( 0.4 \mathrm{T} \)
- C. 0 .65 \)
- D. 0.8 T
Step-by-step solution
Let initial coil have N1=2 turns, radius R1; final coil N2=4 turns, radius R2. Wire length L = N1 * 2πR1 = N2 * 2πR2, so R1 = (N2/N1) R2 = 2R2. Magnetic field at centre B = (μ0 N I)/(2R). Thus B1 = (μ0*2*I)/(2R1) = μ0 I / R1 = 0.2 T. B2 = (μ0*4*I)/(2R2) = 2μ0 I / R2 = 2μ0 I / (R1/2) = 4μ0 I / R1 = 4×0.2 = 0.8 T.
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