The idea is to explain how could we induce current in a flexible loop using an initially free-of-current wire.
The current has to be the same all the way around (otherwise charge would be gathered at some point and in that accumulation of charge, the electric field would point in a way that the flow would even out).
The two forces involved in driving the current around the loop are the source force (typically a battery) and the electrostatic force, which smooths out the flow. The line integral of the vector sum of the previous forces is known as electromotive force (emf).
My answer to the problem
My difficulty in this problem is that I do not have clear the sketch. I would say that the following happens:
Imagine that the loop is in the xy plane. The velocity of the current is tangential to the loop and its direction is clockwise; $B$ will point in the $-z$ direction and the force will point radially outwards. This force would be the source one (provided by the battery and the one that does work to move the loop; I know magnetic force does no work; the individual radial vectors of the force do work but the net work done by all of them is zero) if the wire were just connected to a battery. I also understand that the net electrostatic force is zero (this is a closed path).
But here there is no battery, the current is induced by a change in the current of the wire
My intuition tells me that is the change in the current of the wire what changes the flux of the wire and the changing flux induces the emf in the loop. But not really sure of this...
What's the nature of the induced current in the loop?
EDIT: The original exercise does not provide details on the set up, but my interpretation was the following: we start with two free-of-current wires: one is a loop, the other a straight line. We apply current on the straight wire, which induces an emf on the loop (which will stretch into a circle; this idea came from one of the sources I checked: https://physics.stackexchange.com/questions/239591/magnetic-potential-energy ).
Introduction to Electrodynamics by David Griffiths