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प्रश्न
A rod of length l rotates with a 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 two ends of the rod is ___________ .
विकल्प
zero
`1/2Blomega^2`
Blω2
2Blω2
उत्तर
zero
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 small element of the rod because of its motion is given by
`de = Bomegaxdx`
The emf induced between the centre of the rod and one of its end is given by
\[\int de = \int_0^l B\omega xdx\]
\[ \Rightarrow e = B\omega \left[ \frac{x^2}{2} \right]_0^{l/2} \]
\[ \Rightarrow e = \frac{1}{8}B\omega l^2\]
The emf at both ends is the same. So, the potential difference between the two ends is zero.
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