GATE EC 1993 Electromagnetics Solution Q 3

GATE EC 1993 Electromagnetics Solution Q 3

A long solenoid of radius R, and having N turns per unit length carries a time-dependent current I\left(t\right)=I_0\cos\left(\omega t\right) . The magnitude of the induced electric field at a distance R/2 radially from the axis of the solenoid is

a) \frac R2\mu_0NI_0\;\omega\;\sin\;\left(\omega t\right)

b) \frac R4\mu_0NI_0\omega\;\cos\;\left(\omega t\right)

c) \frac R4\mu_0NI_0\;\omega\;\sin\;\left(\omega t\right)

d) R\mu_0NI_0\;\omega\;\sin\;\left(\omega t\right)

Ans-c)

Explanation

\begin{array}{l}H=NI\left(t\right)\\B=\mu_0\left(H\right)=\mu_0NI\left(t\right)\\B=\mu_0NI_0\cos\left(\omega t\right)\end{array}

According to Stoke’s theorem, we have

\oint E\cdot\overrightarrow{dl}=-\int\frac{\partial\overrightarrow B}{\partial t}\cdot\overrightarrow{ds}
GATE EC 1993 Electromagnetics Solution img2 - Grad Plus
E\cdot2\pi\frac R2=\mu_0NI_0\omega\sin\left(\omega t\right)\frac{\pi R^2}4 E=\frac R4\mu_0NI_0\omega\sin\left(\omega t\right)

Become PRO At Electromagnetics Basics With Our 4 Ultimate Visual FREE E-Books On Coordinate Systems & Transformations

GET THEM NOW!

MORE QUESTIONS

Sign up for our Newsletter

Scroll to Top

NAGPUR UNIVERSITY

PUNE UNIVERSITY

MUMBAI UNIVERSITY