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A solenoid carries a constant current i. An iron rod is slowly inserted into the solenoid along its axis. Which of the following quantities increase as a result?

1. magnetic field at the centre
2. magnetic flux linked with the solenoid
3. self-inductance of the solenoid
4. rate of Joule heating

Correct answer: magnetic field at the centre

Solution

When an iron rod is inserted into a solenoid carrying constant current: (1) Magnetic field B = mu0*mu_r*n*i increases because mu_r >> 1 for iron. (2) Magnetic flux Phi = B*A*N increases proportionally. (3) Self-inductance L = mu0*mu_r*n²*V increases. (4) Rate of Joule heating = i²*R; since i is held constant by the current source and resistance R of the wire is unchanged, Joule heating does NOT increase. Options A, B, and C all increase.

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