Question

The magnetic flux near the axis and inside the air-core solenoid of length $60 \, cm$ carrying current $I$ is $1.57\times 10^{6} \, Wb.$ Its magnetic moment will be (cross-sectional area of a solenoid is very small as compared to its length, $\mu _{0}=4\pi \times 10^{- 7}$ SI units)

• A. $0.25 \, A m^{2}$
• B. $0.5 \, A m^{2}$
• C. $0.75 \, A m^{2}$
• D. $1 \, A m^{2}$

Answer 1

Answer: (C)

Magnetic induction inside the solenoid
$B=\frac{\mu _{0} N I}{L}$
Magnetic flux, $\phi=BA$
$=\frac{\mu _{0} \, N I A}{L}$
Magnetic moment $=NIA=\frac{\phi L}{\mu _{0}}$
$=\frac{1.57 \times 10^{- 6} \times 0.6}{4 \times 3.14 \times 10^{- 7}}$
$=0.75 \, Am^{2}$