Question

The magnetic field ((B)) inside a long solenoid carrying current ' (i) ' with an iron core is (( \mu_0 =) vacuum permeability, (\chi =) susceptibility)

• A. (\mu_0 ni(1 + \chi))
• B. (\mu_0 ni^2(1 + \chi))
• C. (\mu_0 ni\chi)
• D. (\mu_0 ni(1 - \chi))

Hint:

Ferromagnetic cores significantly increase the magnetic field of a solenoid because $\chi$ is very large.

Answer 1

The Correct Option is A

Step 1: Solenoid Field
In vacuum, $B_0 = \mu_0 ni$.

Step 2: Core Effect
With a core, $B = \mu ni = \mu_0 \mu_r ni$. The relationship between relative permeability and susceptibility is $\mu_r = 1 + \chi$.

Step 3: Conclusion
$B = \mu_0 ni(1 + \chi)$.
Final Answer: (A)