Electromagnetic Induction · Physics · IAT (IISER)

A charged particle is moving in a circular orbit with radius $r$ and orbital angular frequency $\omega$ in the presence of a magnetic field. The orbit is enclosed within a larger circular metallic frame. The frame is concentric and coplanar with the orbit. The radius of the frame is now gradually decreased. Assuming that the particle remains within the frame at all times, what changes to the trajectory of the particle will occur as the frame is being shrunk?

Consider an infinite one-dimensional wire carrying a uniform current $I$ as shown in the figure. A square loop of side $a$ is initially placed such that the center of the loop is at a distance $R$ from the wire, where $R>\frac{a}{2}$. The square loop is then moved rightwards with a uniform speed as shown in the figure. What is the induced emf in the loop as a function of time $t$ ?