(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 (\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.

 

 

 
 
 
 
 

Answers (1)
S safeer

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

            \phi =N\vec{B}.\vec{A}

OR

            \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,

             \varepsilon _{0}=NBA\omega

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

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

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

           i_{0}=\frac{NBA\omega }{R}

  • The graph representing the variation of induced emf sVS angle of rotation (\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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