Question

A conducing loop in the shape of a right angled isosceles triangle of height $10cm$ is kept such that the ${90}^o$ vertex is very close to an infinitely long conducting wire (see the figure). The wire is electricity insulted from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangle loop is in counterclockwise direction and increased at a constant rate of $10A{s}^{-1}$.Which of the following statement(s) is(are) true?

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

Answer 1

Answer: (A), (D)

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

Emf induced in wire due to loop will be equal to emf induced in loop due to wire if some amount of current flow and vacation is same.

$\therefore \frac{x}{y}=\frac{10}{10}\Rightarrow x=\frac{y}{z}$.

$\varphi =\int d\varphi ={\int }_0^{0.10}\frac{{\mu }_{0}j}{2\pi y}dx$

$=\frac{0.1{\mu }_{0}i}{\pi }$

$E=\frac{d\varphi }{dt}=\frac{0.1{\mu }_0}{\pi }\frac{d\varphi }{dt}$

$=\frac{{\mu }_0}{\pi }$

clearly force in loop will be repulsive.

So right ans is $A$ and $D$