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JEE Main 2013 · Rotating Conductors & AC Generator

Rotating Conductors & AC Generator question from JEE Main 2013

Q33JEE Main 2013Medium

Rotating Conductors & AC Generator

A metallic rod of length ′ℓ′'\ell' is tied to a string of length 2ℓ2\ell and made to rotate with angular speed ω\omega on a horizontal table with one end of the string fixed. If there is a vertical magnetic field ′B′'B' in the region, the e.m.fe.m.f induced across the ends of the rod is

Figure

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Answer: (d)

  1. The rod lies between distances 2ℓ2\ell and 3ℓ3\ell from the fixed point of rotation.
  2. e=∫2ℓ3ℓBωr dr=12Bω[(3ℓ)2−(2ℓ)2]e = \int_{2\ell}^{3\ell} B\omega r\,dr = \frac{1}{2}B\omega\left[(3\ell)^2 - (2\ell)^2\right]
  3. e=12Bω(9ℓ2−4ℓ2)=5Bωℓ22e = \frac{1}{2}B\omega(9\ell^2 - 4\ell^2) = \frac{5B\omega\ell^2}{2}
  4. So the answer is (d) 5Bωℓ22\frac{5B\omega\ell^2}{2}.
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