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  4. A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad /s about an axis normal to the rod passing through its one end. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. The emf developed across the ends of the rod is

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Q. A $1.0\, m$ long metallic rod is rotated with an angular frequency of $400 \,rad /s$ about an axis normal to the rod passing through its one end. A constant and uniform magnetic field of $0.5\, T$ parallel to the axis exists everywhere. The emf developed across the ends of the rod is

AMUAMU 2011Electromagnetic Induction

Solution:

The emf developed across the ends of the rod
$e=\frac{1}{2} B l^{2} \omega$
$=\frac{1}{2} \times 0.5 \times(1)^{2} \times 400$
$=100\, V$