A wire of mass m and length l can slide freely on a pair of smooth, vertical rails. A magnetic field B exists in the region in the direction perpendicular to the plane of the rails. The rails are connected at the top end by a capacitor of capacitance C. Find the acceleration of the wire neglecting any electric resistance.

Explanation

Let the rod has a velocity `'theta'` at any instant, then at the point, e=Bltheta `
` Now q=cxx potential =ce=cBl theta`
` Current =(dq)/(dt)= cBl theta `
` =cBl (d theta)/(dt)= cBla`
(where a `rarr `acceleration )
From given figure force due to magnetic field and gravity are opposite to each other .
`so, mg-ilB=ma`
` implies mg-cBlaxxlB=ma`
`implies ma+cB^2l^2a=mg`
`implies a(m=cB^2l^2)=mg`
` implies (mg)/(m+cB^2l^2)`.