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.
• B. self-inductance of the solenoid.
• C. magnetic flux linked with the solenoid.
• D. rate of Joule heating.

Answer 1

The correct option is D

rate of Joule heating.

The explanation for the correct option:

Option (D): Rate of Joule heating.

1. The Joule heating is solely determined by the current and the resistance.
2. Inserting an iron rod has no influence on the solenoid's current or resistance.
3. As a result, joule heating is unaffected.
4. Hence, option D is correct.

The explanation for the incorrect answer:

Option(A): The magnetic field at the center.

1. Inserting an iron rod into a magnetic coil increases the magnetic field in the magnetic coil due to the high magnetic permeability of iron.
2. Hence, option A is incorrect.

Option (B): Self-inductance of the solenoid.

1. 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.
2. $L=2{\mu }_{o}nV$
3. Hence, option B is incorrect.

Option (C): Magnetic flux linked with the solenoid.

1. Since magnetic flux($\phi$) is directly proportional to the magnetic field($B$) given as, $\phi =BA\cos \theta$
2. As the magnetic field changes so is the flux.
3. Hence, option C is incorrect.

Hence, option D is the correct option.