Question

The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1.2 × 10^–5. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

• A. 1.2 × 10^–5
• B. 1.2 × 10^–3
• C. 1.8 × 10^–3
• D. 2.4 × 10^–5

Answer 1

The Correct Option is A

To find the fractional increase in the magnetic field inside a solenoid when filled with a magnetic material, we need to understand the effect of magnetic susceptibility on the magnetic field inside the solenoid.

1. **Magnetic Field Inside a Solenoid:** 

For a solenoid with air inside, the magnetic field \(B_0\) is given by:

\(B_0 = \mu_0 \cdot n \cdot I\)

where:

• \(\mu_0\) = permeability of free space
• \(n\) = number of turns per unit length of the solenoid
• \(I\) = current through the solenoid

2. **Effect of Magnetic Material:**

When a magnetic material with susceptibility \(\chi_m\) is inserted inside the solenoid, the permeability becomes:

\(\mu = \mu_0 (1 + \chi_m)\)

The new magnetic field \(B\) inside the solenoid is:

\(B = \mu \cdot n \cdot I = \mu_0 (1 + \chi_m) \cdot n \cdot I\)

3. **Fractional Increase in the Magnetic Field:**

The fractional increase in the magnetic field is given by:

\(\text{Fractional increase} = \frac{B - B_0}{B_0} = \frac{\mu_0 (1 + \chi_m) - \mu_0}{\mu_0} = \chi_m\)

Given \(\chi_m = 1.2 \times 10^{-5}\), the fractional increase in the magnetic field is simply this susceptibility value:

\(\text{Fractional increase} = 1.2 \times 10^{-5}\)

Therefore, the correct answer is the fractional increase is \(1.2 \times 10^{-5}\).

Answer 2

The correct answer is (A) : 1.2 × 10^–5
\(\stackrel{→}{B^′}=μ_0(1+X)ni\) in the material
\(\stackrel{→}{B}=μ_0ni\) without material
So fractional increase is
\(\frac{B^′−B}{B}=X=1.2×10^{−5}\)’