Question

A solenoid of length $0.5\, m$ has a radius of $1\, cm$ and is made up of $500$ turns. It carries a current of $5\, A$. What is the magnetic field inside the solenoid?

• A. $6.28 \times 10^{-3} \, T$
• B. $6.28 \times 10^{3} \, T$
• C. $6.28 \times 10^{-5} \, T$
• D. $6.28 \times 10^{5} \, T$

Answer 1

Answer: (A)

The number of turns per unit length is
$n=\frac{500}{0.5}=1000$ turns / m
The length $(l)=0.5 \,m$ and radius $(r)=0.01 \,m$.
Thus, $ l / a=50$ i.e., $l > >a$.
Hence, we can use the long solenoid formula, namely,
$B=\mu_{0} n I=4 \pi \times 10^{-7} \times 10^{3} \times 5$
$=6.28 \times 10^{-3} T$