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Question
A rod of length l rotates with a small but uniform angular velocity ω about its perpendicular bisector. A uniform magnetic field B exists parallel to the axis of rotation. The potential difference between the centre of the rod and an end is ______________ .
Options
Zero
`1/8omegaBl^2`
`1/2omegaBl^2`
Bωl2
Solution
`1/8omegaBl^2`
Let us consider a small element dx at a distance x from the centre of the rod rotating with angular velocity ω about its perpendicular bisector. The emf induced in the rod because of this small element is given by
`de=Bvl=Bomegaxdx`
The emf induced across the centre and end of the rod is given by
`intde=int_0^(l/2)Bomegaxdx`
`rArrE=Bomega[x^2/x]_0^(l/2)`
`rArrE=1/8Bomegal^2`
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