Question

A conducting loop in the shape of a right angled isosceles triangle of height $10$ cm is kept such that the ${90}^{\circ }$ 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 counter clockwise direction and increased at a constant rate of 10 ${As}^{-1}$. Which of the following statement (s) is (are) true?

• A. There is a repulsive force between the wire and the loop
• B. If the loop is rotated at a constant angular speed about the wire, an additional emf of $\left(\frac{{\mu }_0}{\pi }\right)$ volt is induced in the wire
• C. The magnitude of induced emf in the wire is $\left(\frac{{\mu }_0}{\pi }\right)$ volt
• D. The induced current in the wire is in opposite direction to the current along the hypotenuse

Answer 1

Answer: (A), (C)

There is a repulsive force between the wire and the loop
The magnitude of induced emf in the wire is $\left(\frac{{\mu }_0}{\pi }\right)$ volt

Coefficient of mutual inductance $M=\frac{{\mu }_0{l}_0}{\pi }$

$emf=|-M\frac{dI}{dt}|=\frac{{\mu }_0{l}_0}{\pi }10=\frac{{\mu }_0}{\pi }volt$

As per lenz's law, the loop must move away. Hence there must be repulsive force.

Answer is option A and C.