Question

A circular coil, of radius R, is set up with its plane in the yz plane; its centre at the origin and its axis along the x–axis. It carries a constant current I.

A small rectangular lamina, of area ΔA , is set-up with its plane parallel to the yz plane and its ‘centre’ on the x–axis. It is made to move, with a uniform velocity v(= v\(\hat{i}\)). The dependence of the instantaneous induced emf (ε (x)) , in it (when its centre is to a distance x from the origin (x >>R), on x, is best represented by the graph, labelled as graph

(1) P

(2) Q

(3) R

(4) S

Answer 1

(1) P

The set-up, of the ‘system’, is as shown here. 

The magnetic field, due to the current carrying circular coil, at the center of the rectangular lamina (when this center is at a distance x from the origin), is given by

The rectangular lamina, being a small sized one, the magnetic flux, linked with it, can be written as

The instantaneous induced emf, ε(x), would equal

∴ ε(x) varies as (1/x⁴). This corresponds to graph (P).