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Q.

A conducting rod of length l is rotating with constant angular velocity $ω$ about an axis ${OO}^{|}$ in a uniform magnetic field B as shown in figure. The emf induced between ends P and Q will be

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a

\frac{1}{4} B ω l^{2}

b

\frac{1}{2} B ω l^{2}

c

Zero

d

\frac{5}{10} B ω l^{2}

answer is A.

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Detailed Solution

Question Image

emf induced between $O_{1}$ and P is

Emf induced between $O_{1}$ and Q

$e_{O_{1} P} = \frac{1}{2} B {(\frac{1}{4})}^{2} ω = \frac{B l^{2} ω}{32}$

$e_{O_{1} Q} = \frac{1}{2} B {(\frac{3 l}{4})}^{2} ω = \frac{9 B l^{2} ω}{32}$

$e_{PQ} = e_{OQ} - e_{OP}$

$= \frac{9}{32} B l^{2} ω = \frac{B l^{2} ω}{4} = \frac{1}{4} B l^{2} ω$

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A conducting rod of length l is rotating with constant angular velocity ω about an axis OO| in a uniform magnetic field B as shown in figure. The emf induced between ends P and Q will be