Question

A closely wound solenoid, $80\text{cm}$ long has $5$ layers of windings of $400$ turns each. The diameter of the solenoid is $1.8\text{cm}$. If the current carried is $8.0\text{A}$, estimate the magnitude of $B$ inside the solenoid near its centre.

• A. $2.5\times {10}^{-3}\text{T}$
• B. $7.5\times {10}^{-3}\text{T}$
• C. $7.5\times {10}^{-2}\text{T}$
• D. $2.5\times {10}^{-2}\text{T}$

Answer 1

The correct option is D $2.5\times {10}^{-2}\text{T}$

Given:
Length of the solenoid, $l=80\text{cm}=0.8\text{m}$
Diameter of the solenoid, $D=1.8\text{cm}=0.018\text{m}$
Current carried by the solenoid, $i=8.0\text{A}$

There are five layers of windings of $400$ turns each on the solenoid.

$\therefore$ Total number of turns on the solenoid, $N=5\times 400=2000$

The magnitude of the magnetic field inside the solenoid near its centre is given by the relation,

$B=\frac{{\mu }_{0}Ni}{l}$

$B=\frac{4\pi \times {10}^{-7}\times 2000\times 8}{0.8}$

$\therefore B=2.5\times {10}^{-2}\text{T}$

Hence, option $\left(d\right)$ is correct.