Question

A semicircle conducting ring of radius R is placed in the xy plane, as shown in the figure. A uniform magnetic field is set up along the x-axis. No emf, will be induced in the ring if

• A. it moves along the xaxis
• B. it moves along the yaxis
• C. it moves along the z-axis
• D. All the above

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A it moves along the xaxis
B it moves along the yaxis
C it moves along the z-axis
D All the above

emf induced (by lenz's law)
$\begin{array}{c}E=\frac{-d\varphi }{dt}\\ E=\frac{-d}{dt}\left(BA\right)=-B\frac{d}{dt}\left(A\right)-A\frac{d}{dt}\left(B\right)\end{array}$
either magnetic field or area must be changed w.r.t. time to generate emf, and here the magnetic field and plane of ring are parallel thus no emf induced in either situation.