Question

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

• A. $3.521\times {10}^{-3}T$
• B. $2.521\times {10}^{-3}T$
• C. $3.521\times {10}^{-5}T$
• D. $2.512\times {10}^{-2}T$

Answer 1

The correct option is D $2.512\times {10}^{-2}T$

Length of the solenoid, $l=80$ cm $=0.8$ m

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

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

Diameter of the solenoid, $D=1.8$ cm $=0.018$ m

Current carried by the solenoid, $I=8.0$ A

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

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

where ${\mu }_0$ is the permeability of free space$=4\pi \times {10}^{-7}$Tm$A^{-1}$

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

$=8\pi \times {10}^{-3}$

$=2.512\times {10}^{-2}$T

Hence, the magnitude of the magnetic field inside the solenoid near its centre is $2.512\times {10}^{-2}$ T.