Question

# A constant current $I$ is maintained in a solenoid. Which of the following quantities will not increase if an iron rod is inserted in the solenoid along its axis?

A

the magnetic field at the centre.

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B

self-inductance of the solenoid.

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C

magnetic flux linked with the solenoid.

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D

rate of Joule heating.

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Solution

## The correct option is D rate of Joule heating.The explanation for the correct option:Option (D): Rate of Joule heating.The Joule heating is solely determined by the current and the resistance. Inserting an iron rod has no influence on the solenoid's current or resistance. As a result, joule heating is unaffected.Hence, option D is correct.The explanation for the incorrect answer:Option(A): The magnetic field at the center.Inserting an iron rod into a magnetic coil increases the magnetic field in the magnetic coil due to the high magnetic permeability of iron.Hence, option A is incorrect.Option (B): Self-inductance of the solenoid.Since the self-inductance ($L$) of the coil is directly proportional to the magnetic permeability (${\mu }_{o}$) of the material in the solenoid, the self-inductance of the solenoid also increases.$L=2{\mu }_{o}nV$Hence, option B is incorrect.Option (C): Magnetic flux linked with the solenoid.Since magnetic flux($\phi$) is directly proportional to the magnetic field($B$) given as, $\phi =BA\mathrm{cos}\theta$ As the magnetic field changes so is the flux.Hence, option C is incorrect.Hence, option D is the correct option.

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