The magnetic flux near the axis and inside the air core solenoid of length $60 \mathrm{~cm}$ carrying…

The magnetic flux near the axis and inside the air core solenoid of length $60 \mathrm{~cm}$ carrying current ' $I$ ' is $1.57 \times 10^{-6} \mathrm{~Wb}$. Its magnetic moment will be $\left[\mu_0=4 \pi \times 10^{-7}\right.$, SI unit and cross sectional area is very small as compared to length of solenoid.]
  1. $1 \mathrm{Am}^2$
  2. $0.25 \mathrm{Am}^2$
  3. $0.5\mathrm{Am}^2$
  4. $0.75 \mathrm{Am}^2$

Solution

Magnetic field inside the solenoid is given by $\begin{aligned} & \mathrm{B}=\frac{\mu_0 \mathrm{NI}}{\mathrm{L}} \\ & \therefore \frac{\phi}{\mathrm{A}}=\frac{\mu_0 \mathrm{NI}}{\mathrm{L}} \\ & \therefore \text { Magnetic moment, NIA }=\frac{\phi \mathrm{L}}{\mu_0} \\ & =\frac{1.5 \times 10^{-6} \times 0.6}{4 \times 3.14 \times 10^{-7}} \\ & =0.75 \mathrm{Am}^2 \end{aligned}$

Asked in: MHT CET 2021 (21 Sep Shift 2)

Practice more Electromagnetic Induction questions on Aicharya