JEE Mains · Physics · STD 12 -6. Electromagnetic induction
A metallic rod oflength '\(l\)' is tied to a string oflength \(2l\). and made to rotate with angular speed w on a horizontal table with one end of the string fixed. Ifthere is a vertical magnetic field '\(B\)' in the region, the \(e.m.f.\) induced across the ends of the rod is
- A \(\frac{{2B\omega {l^2}}}{2}\)
- B \(\;\frac{{3B\omega {l^2}}}{2}\)
- C \(\;\frac{{4B\omega {l^2}}}{2}\)
- D \(\;\frac{{5B\omega {l^2}}}{2}\)
Answer & Solution
Correct Answer
(D) \(\;\frac{{5B\omega {l^2}}}{2}\)
Step-by-step Solution
Detailed explanation
Here, induced \(e.m.f.\) \(e=\int_{2 f}^{3 \ell}(\omega x) B d x=B \omega \frac{\left[(3 \ell)^{2}-(2 \ell)^{2}\right]}{2}=\frac{5 B \ell^{2} \omega}{2}\)
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