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Q6.4 A rectangular wire loop of sides $8 cm$ and $2cm$ with a small cut is moving out of a region of uniform magnetic field of magnitude $0.3T$ directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is $1 cm s^{-1}$ in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case?

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Given:

Length of rectangular loop :

$l=8cm=0.08m$

Width of the rectangular loop:

$b=2cm=0.02m$

Area of the rectangular loop:

$A=l*b=(0.08)(0.02)m^2=16*10^{-4}m^2$

Strength of the magnetic field

$B=0.3T$

The velocity of the loop :

$v=1cm/s=0.01m/s$

NOW,

a) Induced emf in long side wire of rectangle:

$e=Blv=0.3*0.08*0.01=2.4*10^{-4}V$

this emf will be induced till the loop gets out of the magnetic field, so

time for which emf will induce :

$t=\frac{distnce }{velocity}=\frac{b}{v}=\frac{2*10^{-2}}{0.01}=2s$

Hence a $2.4*10^{-4}V$ emf will be induced for 2 seconds.

b) Induced emf when we move along the width of the rectangle:

$e=Bbv=0.3*0.02*0.01=6*10^{-5}V$

time for which emf will induce :

$t=\frac{distnce }{velocity}=\frac{l}{v}=\frac{8*10^{-2}}{0.01}=8s$

Hence a $6*10^{-5}V$ emf will induce for 8 seconds.

Posted by

Pankaj Sanodiya

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