Question

A rod of length $10cm$ made up of conducting and non conducting material (shaded part in non –conducting). The rod is rotted with constant angular velocity $10rad/\sec $ about point O, in contact magnetic field of $2$ tesla as shown in figure. The induced Emf between the point A and B of rod will be?

Answer 1

Hint:In this type of question first we have to analyze what is given in question and figure then, using given information and formulae for finding Emf of non conducting material will find the equation and then integrate using values for initial and final as given.

     

Complete step-by-step answer:
Given length of the rod $1=10cm$
Magnetic field $B=2T$
And regular speed $\omega =10rad/\sec $
Considering an element length dr at a distance X from end O.
Emf experienced by the elementary length of the conductor.
$d\varepsilon =BVdx$
Where,
$v=\omega r$
Thus the above equation becomes
$d\varepsilon =B\omega rdr$
Now, potential difference between the point A and B is
$\varepsilon =\int{_{0.07}^{0.01}Bwdr}$
Simplifying it by solving integration,
We get,
$=Bw{{\dfrac{r}{{{2}_{0.07}}}}^{{{2}^{0.1}}}}$
Solving,
$2\times 10\times \dfrac{\left( {{0.1}^{2}}-{{0.07}^{2}} \right)}{2}$
Therefore the final answer is
$\Rightarrow 0.051V$

Note: In this type of problem remember the formulae and values for integration.
Note that it is used to find the length of the conductor.