EMF and magnetic force on a wire moving through a magnetic field

[Nomadyb]

Homework Statement

In the figure, there is a parallel capacitor with capacitance 𝐶 on the upper side,
conductor rail pairs are observed. The capacitor is initially unloaded. Mass 𝑚,
a conductive wire with a length of 𝑙 is frictionless on the rails
it's slipping. A uniform magnetic field in the horizontal direction, as in the figure
it is implemented (from the uppers plane inward). Conductor wire with rails
its resistance is zero. Conductive wire, 𝑡 = 0 instantly released from the top of the rails
it is released and begins to move under gravity.

Relevant Equations

any thing

a) the EMF of ℰ induced on The Wire, as a function of the speed 𝑣of the wire
you can find it.
b) flow induced in the wire𝑖, 𝐶, 𝐵, and are denominated in 𝑙 𝑎 (𝑎= the acceleration of the wire).
c) find the magnetic force acting on the wire in𝐶,𝐵, 𝑙 and𝑎.
d) 𝑎 acceleration, 𝑚, 𝑔, 𝑙, and are denominated in𝐵𝐶.

 

[Delta2]

Hi and welcome to PF

Per forum rules you got to post your best attempt for solution for this problem and then we are allowed to help you with more specific help/hints/what is exactly wrong e.t.c

i suppose for a) you know the answer cause it is a well known problem dealt in many textbooks.
for b) write Kirchoff's Voltage Law for the loop consisting of the capacitor and the moving conductor. You should be able to find the charge on the capacitor as a function of the velocity of the moving conductor. Just take the time derivative of the charge and that is equal to the current.
for c) it is easy once you know b) and the BIL force law (Laplace Force)
for d) write Newton's 2nd law for the moving wire. The answer from c) will come handy in here.

 

[rude man]

3 equations, 3 unknowns and you don't need to solve a differential equation.
P.S. there is no changing B field.