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 figure. The plane of the rails makes an angle θ with the horizontal. A vertical magnetic field B exists in the region. If the wire slides on the rails at a constant speed v, show that



Given:


Length of ab = l


Mass = m


Resistance of ab = R


Angle between the plane of the rails and the horizontal = θ


Magnetic field = B


Velocity with which the wire slides along the rails = v


Diagram:



Formula used:


Emf induced in the wire ab … (i), where


E = emf, B = magnetic field, l’ = component of l perpendicular to the magnetic field = l cosθ, v = velocity


Magnetic force on ab F = I (l X B), where I = current, l = length of ab, B = magnetic field


Now, the angle between l and B is 900 - θ.


Therefore, F = IlBsin (900 -

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