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JEE Main 2023 (24 Jan, Shift 2) · Rotating Conductors & AC Generator

Rotating Conductors & AC Generator question from JEE Main 2023 (24 Jan, Shift 2)

Q19JEE Main 2023 · 24 JAN · SHIFT 2Easy

Rotating Conductors & AC Generator

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 rod as shown in figure. The induced emf will be:

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Answer: (b)

Each element $dx$ at distance $x$ has speed $\omega x$ : $de = B\omega x\,dx$ .
$e = \int_0^L B\omega x\,dx = \tfrac{1}{2}BL^2\omega$
So the answer is (b) $\tfrac{1}{2}BL^2\omega$ .

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