Answer :


Given:


Edge length of square frame =a


Magnetic field intensity B


Speed of corners of rhombus =u


(a) when the angles at the corner reduce to 60°



We know that,


motional emf produced due to a conductor of length l moving with velocity v in a magnetic field B is given by



Motional emf is produced in each side of rhombus and the effective length of each side is the length perpendicular to velocity of corners.


From the fig. the effective length of each side is



Since velocity is perpendicular to magnetic field the equation of emf induced in each side given by



Total emf induced in all four side is



Therefore, induced emf in the frame when the angles at the corner reduces to 60° is 2uBa


(b) total resistance of the frame =R


hence current flowing in the frame is



Therefore, current flowing in the frame at this instant is 2uBa/R


(c) initially the frame is in form of square of side a and area


at this time flux through this frame is given by



Finally, when the frame reduces to straight line flux passing through the frame reduces to zero



Average emf induced in the frame in time t is given by



The current flowing through the frame is then given by



Where R is the resistance of frame


Hence the charge (Q) flowing through the side of frame in time t is



Therefore total charge flowing through side of frame by the time the frame reduces to straight line is


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