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Standard XII

Physics

Motional EMF

A metal rod o...

Question

A metal rod of length $15 \times 10^{- 2} m$ rotates about an axis passing through one end with a uniform angular velocity of $60 r a d s^{- 1}$ . A uniform magnetic field of $0.1$ . Tesla exists in the direction of the axis of rotation. Calculate the EMF induced between the ends of the rod.

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Solution

As shown in the figure,the speed of center of mass of rod is $V$ .
$V = ω \frac{l}{2}$
where, $l$ =length of rod
$V = \frac{60 \times 15 \times 10^{- 2}}{2} = 4.5 m s^{- 1}$
emf induced $e = V B l = 4.5 \times 0.1 \times 15 \times 10^{- 2}$
$e = 0.0675 V$

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A metal rod of length 15×10−2m rotates about an axis passing through one end with a uniform angular velocity of 60 rad s−1. A uniform magnetic field of 0.1. Tesla exists in the direction of the axis of rotation. Calculate the EMF induced between the ends of the rod.

As shown in the figure,the speed of center of mass of rod is V.V=ωl2where, l=length of rodV=60×15×10−22=4.5ms−1emf induced e=VBl=4.5×0.1×15×10−2e=0.0675V

A metal rod of length $15 \times 10^{- 2} m$ rotates about an axis passing through one end with a uniform angular velocity of $60 r a d s^{- 1}$ . A uniform magnetic field of $0.1$ . Tesla exists in the direction of the axis of rotation. Calculate the EMF induced between the ends of the rod.

As shown in the figure,the speed of center of mass of rod is $V$ .
$V = ω \frac{l}{2}$
where, $l$ =length of rod
$V = \frac{60 \times 15 \times 10^{- 2}}{2} = 4.5 m s^{- 1}$
emf induced $e = V B l = 4.5 \times 0.1 \times 15 \times 10^{- 2}$
$e = 0.0675 V$