Q.

A right angled triangular loop as shown below enters uniform magnetic field (at right angle to the boundary of the field) directed into the paper. Draw the graph between induced emf e and the distance along the perpendicular to the boundary of the field, (say x) along which loop moves.

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a

b

c

d

answer is C.

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Detailed Solution

For 0≤x≤a, ϕ=12Bx2 e=-dϕdt=-Bav At x=0,e=0 At x=a/2, e=-Bav2 At x=x→a,e≈-Bav As x=a,e=0 ϕ=constant For a≤x≤2a        ϕ=12Ba2=constant For 2a≤x≤3a, ϕ=Ba22-x122 e=-dϕdt=-ddtB2a2-x12=Bx1v At x1=0, e=0 At x1=a/2,e=B2avAt x1=a,e=0, loop is outside the field.
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