Electromagnetic Induction

JEE Main level, numerical answer, medium

82 of 153

Question 82 of 153

A 20cm20cm long metallic rod is rotated with 210rpm210rpm about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field 0.2T0.2T parallel to the axis exists everywhere. The emf developed between the centre and the ring is _________mVmV.
(Take π=227\pi =\dfrac{22}{7})

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Answer: 88

The data given is
ω=210×2π60rads−1=7πrads−1l=0.2mB=0.2T\omega =210\times \dfrac{2\pi }{60}rad{s}^{-1}=7\pi rad{s}^{-1} l=0.2m B=0.2T
The emf is given by
ϵ=Bωl22\epsilon =\dfrac{B\omega {l}^{2}}{2}
=0.2×7π×(0.2)22=0.2\times 7\pi \times \dfrac{{\left(0.2\right)}^{2}}{2}
=88mV=88mV

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