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A metallic rod of length l is tied to a string of length 2 l a

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A metallic rod of length $l$ is tied to a string of length $2 l$ and made to rotate with angular speed $ω$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $B$ in the region, the emf induced across the ends of the rod is

\frac{2 B ω l ^{3}}{2}

\frac{3 B ω l ^{3}}{2}

\frac{4 B ω l ^{2}}{2}

\frac{5 B ω l ^{2}}{2}

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Updated on: May 4, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2013

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A metallic rod of length

l

is tied to a string of length

2 l

and made to rotate with angular speed

ω

on a horizontal table with one end of the string fixed. If there is a vertical magnetic field

B

in the region, the emf induced across the ends of the rod is

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

∵

Induced emf is rate of change of magnetic flux.
Solution Image

e = \int B v d x [∵ v = ω x] \Rightarrow e = \int_{2 l}^{3 l} (ω x) \cdot B \cdot d x Using \int x^{n} d x = \frac{x ^{n + 1}}{n + 1} \Rightarrow e = B ω [\frac{x ^{2}}{2}]_{2 l}^{3 l} e = B ω \frac{[ ( 3 l ) ^{2} - ( 2 l ) ^{2} ]}{2} = \frac{5 B l ^{2} ω}{2}

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Question Text	A metallic rod of length $l$ is tied to a string of length $2 l$ and made to rotate with angular speed $ω$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $B$ in the region, the emf induced across the ends of the rod is
Updated On	May 4, 2023
Topic	Magnetism and Matter
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 3
Upvotes	385
Avg. Video Duration	5 min

A metallic rod of length $l$ is tied to a string of length $2 l$ and made to rotate with angular speed $ω$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $B$ in the region, the emf induced across the ends of the rod is

Text solutionVerified

Filo tutor solutions (3)

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A metallic rod of length l is tied to a string of length 2l and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the emf induced across the ends of the rod is

Text solutionVerified

Filo tutor solutions (3)

Questions from JEE Mains 2013 - PYQs

Practice questions from Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Practice questions from Magnetism and Matter in the same exam

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A metallic rod of length $l$ is tied to a string of length $2 l$ and made to rotate with angular speed $ω$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $B$ in the region, the emf induced across the ends of the rod is