Shown a metallic square frame of edga a in a vertical plane. A uniform magnetic field B exists in the space in a directon perpendicular to the plane of the figure. Two boys pull the opposite corners of the square ot deform it into a rhombus. They start pulling the corners t t=0 and sisplace the corners at a uniform speed u. (a) find the induced emf in the frame at the instant when the angles at these corners reduce to `60^@`. (b) find the induced current in the frame at this instatnt if the total resistance of the frame is R. (c) Find the total charge which flows through a side of the frame by the time the square is deformed into a straight line.

Explanation

(a) The perpendicular component i.e a sin theta is to be taken which is perpendicular to velocity`
`So, l=a sin 30^(@) =(a/2)`
`Net 'a' charge =4xx(a/2)=2a`
`So, induced emf= Bul=2auB`
`(b) Current=(e/R)=(2auB)/(R )`