A line charge (lambda per unit length) is in | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) According to Faraday's Law of induction,the changing magnetic flux induces an electric field $E$ along the circumference of the wheel. The induced

Vedclass · Accepted Answer

$\frac{\pi a b^2 \lambda B}{I}$ clockwise as seen from above

Vedclass · Answer

(B) According to Faraday's Law of induction,the changing magnetic flux induces an electric field $E$ along the circumference of the wheel. The induced $EMF$ $\varepsilon$ is given by $\varepsilon = \left| -\frac{d\phi}{dt} ight| = \oint \vec{E} \cdot d\vec{l} = E(2\pi a)$.Since $\phi = B(\pi b^2)$,we have $\varepsilon = \pi b^2 \frac{dB}{dt}$.Equating the two,$E(2\pi a) = \pi b^2 \frac{dB}{dt}$,which gives $E = \frac{b^2}{2a} \frac{dB}{dt}$.The force on the charge element $dq = \lambda(2\pi a)$ is $dF = E dq$. The torque $	au$ is $	au = a F = a(E \cdot 2\pi a \lambda) = 2\pi a^2 \lambda E$.Substituting $E$,$	au = 2\pi a^2 \lambda \left( \frac{b^2}{2a} \frac{dB}{dt} ight) = \pi a b^2 \lambda \frac{dB}{dt}$.Using $	au = I \frac{d\omega}{dt}$,we have $I \frac{d\omega}{dt} = \pi a b^2 \lambda \frac{dB}{dt}$.Integrating both sides,$I \omega = \pi a b^2 \lambda B$,so $\omega = \frac{\pi a b^2 \lambda B}{I}$.By Lenz's Law,the induced current creates a magnetic field opposing the change. Since the magnetic field is decreasing,the induced electric field will create a torque such that the wheel rotates in the direction that opposes the decrease in flux,which is clockwise as seen from above.

Similar Questions

Discuss Faraday's experiment of bar magnet and coil for generation of electric current in coil.

The magnetic flux through a stationary loop with resistance $R$ varies during an interval of time $T$ as $\phi = at(T - t)$. The heat generated during this time,neglecting the inductance of the loop,will be

The graph shows the magnitude $B(t)$ of a uniform magnetic field that exists throughout a conducting loop,perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop,greatest first.

$A$ coil is placed perpendicular to a magnetic field of $5000 \,T$. When the field is changed to $3000 \,T$ in $2 \,s$, an induced emf of $22 \,V$ is produced in the coil. If the diameter of the coil is $0.02 \,m$, then the number of turns in the coil is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module