| A metallic rod of length\[\ell \] is tied to a string of length\[2\ell \]and made to rotate with angular speed\[\omega \]on a horizontal table with one end of the string fixed. If there is a vertical magnetic field 'B' in the region, the e.m.f. induced across the ends of the rod is: [JEE MAIN 2013] |
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A) \[\frac{2B\omega {{\ell }^{2}}}{2}\]
B) \[\frac{3B\omega {{\ell }^{2}}}{2}\]
C) \[\frac{4B\omega {{\ell }^{2}}}{2}\]
D) \[\frac{5B\omega {{\ell }^{2}}}{2}\]
Correct Answer: D
Solution :
| [d] \[\int{\left( \vec{v}\times \vec{B} \right)}.\overrightarrow{d\ell }=\int\limits_{2\ell }^{3\ell }{x\omega Bdx}\] |
\[V=\frac{5B\omega {{\ell }^{2}}}{2}\] |
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