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A wire ab of length l, mass m and resist...

A wire ab of length l, mass m and resistance R slides on a smooth thick pair of metallic rails joined at the bottom as shown in fig. The plane of the rails makes an angle `theta` with the horizontal. A vertical magnetic field B exist in the region. If the wire slides on the rails at a constant speed v, then the value of B is -

A

`sqrt((mgR)/(vl^(2)cos^(2)theta))`

B

`sqrt((mgR cos theta)/(vl^(2)sin^(2)theta))`

C

`sqrt((mgR)/(v^(2)l^(2)sin^(2)theta))`

D

`sqrt((mgR sin theta)/(vl^(2)cos^(2)theta))`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • A wire of length l , mass m and resistance R slides without any friction down the parallel conducting rails of negligible resistance . The rails are connected to each other at the bottom by a resistanceless rail parallel to the wire so that the wire and the rails form a closed rectangualr conducting loop. The plane of the rails makes an angle theta with the horizontal and a uniform vertical magnetic field of the inducetion B exists throughout the rregion. Find the steady state velocity of the wire.

    A
    (a) `(mg)/(R )(sin theta)/(B^(2)l^(2)cos^(2)theta)`
    B
    (b) `(mg)/(R )(sin^(2) theta)/(B^(2)l^(2)cos^(2)theta)`
    C
    ( c) `(mgR sin theta)/(B^(2)l^(2)cos^(2)theta)`
    D
    ( d) `mgR (sin^(2) theta)/(B^(2)l^(2)costheta)`

  • A conducting wire ab of length l resistance r and mass m starts sliding down at t=0 on a smooth, vertical thick pair of connected rails as shown. The terminal speed of the wire is

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