Problem 1. Vertical Rails with capacitor Long enough vertical rails distance l f

Question

Problem 1. Vertical Rails with capacitor Long enough vertical rails distance l from each other made of an ideal conductor are connected by a capacitor C. A bar of mass M, also made of an ideal conductor, can slide along the rails without friction and without loosing electrical contact with the rails. A uniform magnetic field B is horizontal and perpendicular to the plane of the rails. At some point the bar was released with zero initial velocity. Initial charge on the capacitor is zero. Find the acceleration of the bar 9

Explanation / Answer

induced voltage V = Blv

magnetic force acting upwards fB = qvB

multiplying above equations

fB*V = qv^2B^2l

from the relation

q = cV

c = q/V

fB = cv^2B^2l

from the kinematic realtion

v = u+at

u = 0

v = gt

fB = cg^2t^2B^2l

total acceelration a =g- fB/M

a= g-cg^2t^2B^2l/M

acceleration is time dependant

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