The figure below shows a bar of mass m that can slide without friction on a pair

Question

The figure below shows a bar of mass m that can slide without friction on a pair of rails separated by a distance and located on an inclined plane that makes an angle with respect to the ground. The resistance of the resistor is R, and a uniform magnetic field of magnitude B is directed downward, perpendicular to the ground, over the entire region through which the bar moves. With what constant speed v does the bar slide along the rails? (Use any variable or symbol stated above along with the following as necessary: g.)
v =   

Explanation / Answer

emf induced e = B*v*L*sin(theta) = B*v*L*costheta

current I = e/R

magnetic force Fb = I*L*B = e*L*B/R = B*v*L*sintheta*L*B/R

Fb = B*L^2*v*sintheta/R up the plane

for constant speed Fnet = 0

Fb + Fg = 0

m*g*sintheta - B*L^2*v*sintheta/R = 0

m*g*sintheta = B*L^2*v*sintheta/R

v = m*g*R*/(B*L^2)     <<<<------answer

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