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A metal wire of mass m slides without fr...

A metal wire of mass m slides without friction on two horizontal rails spaced distance d-apart as shown in figure. The rails are situated in a uniform magnetic field B, directed vertically upwards, and a battery is sending a current I through them. Find the velocity of the wire as a function of time, assuming it to be at rest initially.

Text Solution

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The magnatic force on the wire of length d due to magnetic field is `F=IBd sin 90^@=IBd`
This force, according to Left Hand Rule, acts perpendicular to the wire in the plane of paper towards left hand side. Due to it, the wire moves towards left with the acceleration.
`a=F/m=(IBd)/(m)`
Velocity of the wire at a time t will be
`v=u+at=0+(IBd)/(m)t`
or `v=(IBd)/(m)t` towards left
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