# (a) A rectangular coil rotates in a uniform magnetic field. Obtain an expression for induced emf and current at any instant. Also find their peak values. Show the variation of induced emf versus angle of rotation $\inline (\omega t)$ on a graph.(b) An iron bar falling through the hollow region of a thick cylindrical shell made of copper experiences a retarding force. What can you conclude about the nature of the iron bar ? Explain.

(a) We know, the magnetic flux $(\phi )$ is given as ;

$\phi =N\vec{B}.\vec{A}$

OR

$\inline \phi =NBA\; \cos \omega t$

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

$\varepsilon =-d\frac{\left ( N\vec{B}\vec{A}\cos \omega t \right )}{dt}$

$\varepsilon =NBA\omega \sin \omega t$

We know,

$\inline \varepsilon _{0}=NBA\omega$

So, On replacing the value of $\inline NBA\omega$ by $\inline \varepsilon _{0}$, we have

$\inline \varepsilon =\varepsilon _{0}\; \sin \omega t$

$\inline i=\frac{\varepsilon }{R}=\frac{NBA\omega \sin \omega t}{R}$

$\inline i_{0}=\frac{NBA\omega }{R}$

• The graph representing the variation of induced emf sVS angle of rotation $\inline (\omega t)$ ;-

(b) The iron bar is a magnet and we know that when the bar magnet falls through the shell made up of copper, it produced a change in magnetic flux through it. Hence, the induced emf opposes the cause. (this is according to the Lenz's law) and hence bar experiences a retarding force.

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