1. Tardigrade
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  4. A horizontal wire free to slide on the vertical rails of a conducting frame as shown in figure. The wire has a mass m and length ℓ and the resistance of the circuit is R. If a uniform magnetic field B is directed perpendicular to the frame, then find the terminal speed of the wire as it falls under the force of gravity, in m/s. ( m =1 kg , R =1 Ω, B =1 T , ℓ=√2 m )

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Q. A horizontal wire free to slide on the vertical rails of a conducting frame as shown in figure. The wire has a mass $m$ and length $\ell$ and the resistance of the circuit is $R$. If a uniform magnetic field $B$ is directed perpendicular to the frame, then find the terminal speed of the wire as it falls under the force of gravity, in m/s. $( m =1\, kg , R =1\, \Omega, B =1\, T , \ell=\sqrt{2}\, m )$Physics Question Image

Electromagnetic Induction

Solution:

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Power by ext. force $=$ Rate of change of $KE +$ electrical power
As wire is moving with terminal velocity its $KE =$ constant
$m g v T=i^{2} R$
$mgv_{ T } =\left(\frac{ B \ell v _{ T }}{ R }\right)^{2} \times R$
$mg =\frac{ B ^{2} \ell^{2} v _{ T }}{ R }$
$v _{ T } =\frac{ mgR }{ B ^{2} \ell^{2}}$