# 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.

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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