Question

A solenoid $4cm$ in diameter and $20cm$ in length has $250$ turns and carries a current of $15A$. Calculate the flux through the surface of a disc of $10cm$ radius that is positioned perpendicular to and centred on the axis of the solenoid.

Answer 1

R = radius of solenoid = 2 cm

$L=20cm$, $turns=N=250$

turns per unit length = $n=1,250turns/meter$

current $i=15A$

Magnetic field through the solenoid = ${\mu }_{0}ni=4\pi \times {10}^{-7}\times 1250\times 15units$

$B=2.356\times {10}^{-2}H$

The magnetic field outside the turns of the solenoid is zero, ie., it exists only in the area of $\pi r^2$

$Flux=B\times \pi r^2=0.0185volt\sec$