A square loop of side 10 cm with its side parallel to X and Y axes is moved with a velocity of 8 cm s-1 in the positive X - direction containing a magnetic field in positive Z - direction. The field is non - uniform and has a gardient of 10^{-3}T cm -1 along the negative X - direction (i.e. it increases by 10^{-3}T cm -1 as one moves in the negative X- direction). Calculate the emf induced.

 

 

 

 
 
 
 
 

Answers (1)
S safeer

Given,

Side of square loop, l = 10cm = 0.10m

Area of loop = 0.10 \times 0.10 = 100 \times 10^{-4}m^{2}

Velocity of the loop in the positive x- direction = 8cm =  0.08 m/s

Gradient of magnetic field in negative x-directioin = \frac{dB}{dx}= 10^{-3} T /cm= 10^{-1} T /m

So, induced emf due to changing positon  = \frac{d\phi }{dt}= \frac{d(BA)}{dt}= \frac{AdB}{dx}\frac{dx}{dt}

                                                                  = \frac{AdB}{dx}V

                                                                =100 \times 10^{-4}\times 10 ^{-1}\times 0.08

                                                                =0.8 \times 10^{-4}V

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