Answer to Question #129967 in Electricity and Magnetism for Rimsha Ahmed

Question

An aluminium disc of radius r rotated about its centre at a constant speed. It is placed in a uniform magnetic field perpendicular to its surface. A steady electromotive force (e.m.f.) E is generated between the centre O nd the rim at P.

What is the e.m.f. generated between points Q and R, each a distance r/2 from the centre?

A. Zero
B. E/4
C. E/2
D. E

It's answer is given "A. Zero" in the book.
Kindly explain why the answer must be zero, please.

Thank you.

Answer 1

We know that the emf = rate of change of magnetic flux.

$e=-\frac{d\phi}{dt}$

where $\phi =$ magnetic flux.

$\phi= B. A$

Where B is the magnetic field and A is the area of the disc.

But as per the question's requirement, magnetic field is constant and the area of the loop is constant, hence the value of flux will be constant.

The differentiation of the constant terms is always constant.

Hence $\dfrac{d\phi}{dt}=0$

Hence the value of emf will be zero.