Question

A wire loop in the shape of a rectangle of length L and width W and a Long and straigh Wire carries a current I. As shown in the picture. 
A) Determines the Magnetic flow through The turn by the Current I.
b) Suppose the current changes over time according to the Equation I = a + bt, where a and b are constants. Determine the induced emf in the loop if B=10A/s;  h=1cm; w=10cm and L=100cm
c) What is the direction of the induced current in the rectangle?

ANSWERS ARE ALSO SHOWN IN THE PICTURE.

Thanks!

Sol: a) Aion Inch w 2n AOL ln( 2n c) 4.8 HV

Answer 1

magnetic field at a point r from wire = B = uo*I/(2*pi*r)

consider a small area of widht dr and length w

small area dA = L*dr

magnetic flux through the small area dphi = B*dA = uo*I*L*dr/(2*pi*r)

total flux phi = integral dphi from r1 = h to r2 = h+w

phi = (mu0*I*L/(2*pi))*ln(r2/r1)

I L

phi = (mu0*I*L/(2*pi))*ln((h+w)/h)

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(b)

induced EMF = -rate of change in flux

E = -(d/dt)*phi

E = -(mu0*L/(2*pi))*ln((h+w)/h)*((dI)/(dt))

pt0 In h dt

=========================

(c)

dI/dt = b

E = -(mu0*L/(2*pi))*ln((h+w)/h)*(b)

E = -(4*pi*10^-7*1/(2*pi))*ln(0.11/0.01)*10

E = -4.8 u V