Ques 15
Asked by rbhatt16
23rd August 2018,
6:25 PM
Answered by Expert
Answer:
induced emf ξ in the loop-A is given by, ξ = 
,
, φ is the magnetic flux which is given by φ = B×A, where B is magnetic field and A is area of coil.
hence we have ξ = - A (dB/dt) .............(1)
induced emf ξ in the loop-A, when it is moving towards loop-B is written as, ξ = - A (dB/dt) = -A (dB/dx)(dx/dt) = -Av(dB/dx) ...........(2)
where v is speed of movement of loop-A and x is the distance from the centre of loop-B .
Magnetic field B along the axis of loop-B = 
,
,where R is radius of loop-B, I is the current passing through the loop-B and x is the distance of point in the axis from centre of loop
slope of magnetic field = dB/dx = 
the slope dB/dx is maximum at x, where the function f(x) = 
is maximum.
is maximum. the distance x at which the slope of field is maximum can be determined by solving for x in the equation df(x)/dx = 0.
It is expected from the student to do this exercise and find that df(x)/dx is maximum at x = R/√2
Since induced emf is proportional to slope dB/dx of magnetic field and this slope is maximum at x = R/√2,
we can conclude that induced emf in loop-A is maximum at R/√2 from the center of loop-B
Answered by Expert
24th August 2018,
2:23 PM
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