Question

An ideal solenoid of 1500 turns/m and radius 0.75 cm, changes its current at the uniform rate of 0.5 As^–1. Now consider a circle inside the solenoid of radius 0.5 cm whose axis coincides with that o solenoid.

Find the electric field induced on the circumference of the circle.

Answer 1

Dear Student,

We know that
$$\begin{gathered} \oint E.dl=-\frac{d\phi }{dt}=-\frac{d\left(BA\right)}{dt}=-A\frac{d\left(B\right)}{dt} \\ ForsolonoidB={\mu }_{0}nI \\ \oint E.dl=-A{\mu }_{0}n\frac{d\left(I\right)}{dt} \\ E2\pi \times 0.5=-\pi \times 0.{75}^2\times 4\pi \times 1500\times 0.5 \\ E=5298.75 \end{gathered}$$
E = 5298.75 *10^-4 = .5298 V/m