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Solved Problems-2

Problem-2
(a) An ac generator consisting of a single square loop of wire, with length of each side being ‘a’, is rotating in a steady magnetic field Description: 16439.png at an angular velocity ‘ω’. The axis of the loop rotation is perpendicular to the uniform field. Find the voltage induced in the loop.
 
(b) If the flux density varies harmonically with time as Description: 18422.png what will be the induced emf for (a)?
Description: 44645.png
AC generator
 
Solution
(a) Here, Description: 19608.png
 
Since, only two sides of the loop cut the flux lines, l = 2a
 
∴ emf induced is,
 
Description: 18969.png
 
where, Description: 17901.png
 
Description: 17169.png
 
(b) In this case, in addition to the motional emf, transformer emf will be induced.
 
From (a), motional emf is,
 
Description: 16535.png
 
Transformer emf is, Description: 18202.png
 
Here, Description: 19524.png
 
and, Description: 19449.png
 
∴ Description: 24032.png
 
So, the total emf induced is,
 
Description: 24036.png
 
Description: 17332.png
 





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