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Q.

A Conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 900 vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of 10 As−1 . Which of the following statement (s) is (are) true?

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a

There is a repulsive force between the wire and the loop

b

The magnitude of induced emf in the wire is μ0π  volt

c

If the loop is rotated at a constant angular speed about the wire, an additional emf  of μ0πvolt is induced in the wire

d

The induced current in the wire is in opposite direction to the current along the hypotenuse

answer is A.

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Detailed Solution

Flux=φ=∫B→⋅dA→=∫00.1 2xdxμ0i2πx=μ0iπ0.1=μ0i10π Also, φ=Mi⇒ Mutual Inductance =M=φi=μ010π Induced emf =ε=Mdidt=μ010π(10)=μ0πAs the current in loop is increased, its flux is trying to increases out of the page. To oppose it, direction of current in wire should be towards right. Since, direction of current in wire is same as direction of current in hypotenuse , force b/w wire & loop is repulsive.As the loop rotates  around the wire flux through it due to current in wire will not change. Hence M will not change. So, no additional emf is generated.
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