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 -