Question

A solenoid of length $0.5m$ has a radius of $1cm$ and is made up of $500$ turns. It carries a current of $5A$. 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 $(l)=0.5m$ and radius $(r)=0.01m$.
Thus, $l/a=50$ i.e., $l>>a$.
Hence, we can use the long solenoid formula, namely,
$B={\mu }_{0}nI=4\pi \times 10^{-7}\times 10^3\times 5$
$=6.28\times 10^{-3}T$