(C) Consider a small element of length '$dx$' at a distance '$x$' from the axis of rotation.The linear velocity of this element is '$v = \omega x$'.Th

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

(C) Consider a small element of length '$dx$' at a distance '$x$' from the axis of rotation.The linear velocity of this element is '$v = \omega x$'.The motional emf induced in this small element is given by '$d\varepsilon = Bv dx = B(\omega x) dx$'.To find the total induced emf,we integrate this expression from '$x = 0$' to '$x = L$':$\varepsilon = \int_0^L B \omega x dx$$\varepsilon = B \omega \int_0^L x dx$$\varepsilon = B \omega \left[ \frac{x^2}{2} \right]_0^L$$\varepsilon = \frac{1}{2} BL^2 \omega$

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

Medium

$A$ metallic rod of length '$L$' is rotated with an angular speed of '$\omega$' normal to a uniform magnetic field '$B$' about an axis passing through one end of the rod,as shown in the figure. The induced emf will be:

JEE MAIN 2023 All JEE MAIN

A
$\frac{1}{4} B^2 L \omega$
B
$\frac{1}{4} BL^2 \omega$
C
$\frac{1}{2} BL^2 \omega$
D
$\frac{1}{2} B^2 L^2 \omega$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Physics Questions

Chapter

Electromagnetic Induction

Subtopic

Motional EMI (Induced Parameter)

Previous Year

JEE MAIN 2023 Paper All JEE MAIN years →

$A$ thin semicircular conducting ring $(PQR)$ of radius $r$ is falling with its plane vertical in a horizontal magnetic field $B,$ as shown in the figure. The potential difference developed across the ring when its speed is $v,$ is

EasyAIPMT 2014

View Solution

$A$ conducting rod $PQ$ of length $L = 1.0\, m$ is moving with a uniform speed $v = 20\, m/s$ in a uniform magnetic field $B = 4.0\, T$ directed into the paper. $A$ capacitor of capacity $C = 10\, \mu F$ is connected as shown in the figure. Then:

Difficult

View Solution

$A$ conducting rod $PQ$ of length $L = 1.0\, m$ is moving with uniform speed $v = 20\, m/s$ in a uniform magnetic field $B = 4.0\, T$ directed into the paper. $A$ capacitor of capacity $C = 10\, \mu F$ is connected as shown in the figure. Then:

Difficult

View Solution

$A$ wheel with $20$ metallic spokes,each $1 \,m$ long,is rotated with a speed of $120 \,rpm$ in a plane perpendicular to a magnetic field of $0.4 \,G$. The induced emf between the axle and the rim of the wheel will be $\left(1 \;G = 10^{-4} \;T \right)$.

MediumNEET 2020

View Solution

$A$ metal rod moves at a constant velocity in a direction perpendicular to its length. $A$ constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement$(s)$ from the following.

EasyIIT 1998

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ metallic rod of length '$L$' is rotated with an angular speed of '$\omega$' normal to a uniform magnetic field '$B$' about an axis passing through one end of the rod,as shown in the figure. The induced emf will be:

Similar Questions

$A$ thin semicircular conducting ring $(PQR)$ of radius $r$ is falling with its plane vertical in a horizontal magnetic field $B,$ as shown in the figure. The potential difference developed across the ring when its speed is $v,$ is

$A$ conducting rod $PQ$ of length $L = 1.0\, m$ is moving with a uniform speed $v = 20\, m/s$ in a uniform magnetic field $B = 4.0\, T$ directed into the paper. $A$ capacitor of capacity $C = 10\, \mu F$ is connected as shown in the figure. Then:

$A$ conducting rod $PQ$ of length $L = 1.0\, m$ is moving with uniform speed $v = 20\, m/s$ in a uniform magnetic field $B = 4.0\, T$ directed into the paper. $A$ capacitor of capacity $C = 10\, \mu F$ is connected as shown in the figure. Then:

$A$ wheel with $20$ metallic spokes,each $1 \,m$ long,is rotated with a speed of $120 \,rpm$ in a plane perpendicular to a magnetic field of $0.4 \,G$. The induced emf between the axle and the rim of the wheel will be $\left(1 \;G = 10^{-4} \;T \right)$.

$A$ metal rod moves at a constant velocity in a direction perpendicular to its length. $A$ constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement$(s)$ from the following.

Vedclass Test Series

Exam Paper Generator

Online Exam Module