Two separate long solenoids, A and B

PHYSICS · Subjective · CBSE · Physics · Moving Charges and Magnetism · Moving Charges and Magnetism

Problem

Two separate long solenoids, A and B, are to be compared. Solenoid A: 600 turns uniformly wound over a length of 0.30 m carrying a current of 4.0 A. Solenoid B: 900 turns uniformly wound over a length of 0.45 m carrying an unknown current IBI_B. (i) Derive an expression for the ratio BABB\dfrac{B_A}{B_B} in terms of the respective numbers of turns, lengths, and currents. (ii) Using the above data, calculate the magnetic field inside solenoid A. (iii) Determine the current IBI_B that must flow through solenoid B so that it produces the same magnetic field as solenoid A. (iv) If both solenoids are operated at the same current of 4.0 A, find the ratio BABB\dfrac{B_A}{B_B} of their magnetic fields.

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