An iron ring of relative permeability \( \mu_r \), is introduced inside a toroidal solenoid having \( \eta \) turns per meter. If the current in the solenoid is I, then the magnetic field in the ring is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \mu_o\mu_r\,\eta\, I \)
Inside a toroid or a long solenoid the field in air is \( B_0 = \mu_0\,n\,I \), where \( n \) is the number of turns per unit length. When the space is filled with a magnetic material of relative permeability \( \mu_r \), the permeability becomes \( \mu = \mu_0\mu_r \).
\( \displaystyle B = \mu_0\,\mu_r\,n\,I \)
With \( n = \eta \) turns per metre, the field in the iron ring is \( \mu_0\mu_r\,\eta\,I \).
Shortcut: Every option contains \( \mu_0\mu_r I \); only the power of \( \eta \) differs. The field is proportional to the number of turns per metre, so the power of \( \eta \) must be 1. Only Option (4) has it.