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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