question_answer

A solid conducting sphere of radius R is moved with a velocity V in a uniform magnetic field of strength B such that \[\overrightarrow{B}\] is perpendicular to \[\overrightarrow{V}\]. The maximum e.m.f. induced between two points of the sphere is:

A) 2 R B V

B) R B V

C) \[\sqrt{2}\,R\,\,B\,\,V\]

D) \[\frac{RBV}{2}\]

Correct Answer: A

Solution :

Consider the diametrical opposite points, A and B then |e| = 2RBV

Alternative solution

Maximum length of a rod perpendicular to v & B is 2R.

\[\therefore \]      \[{{E}_{\max }}=B\,\,2RV.\]