A loop of wire in the shape of a rectangle of width w and length L and a long, s

Question

A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in the figure below.

(a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: 0 and .)
B =  

(b) Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the magnitude of the emf that is induced in the loop if b = 20.0 A/s, h = 1.00 cm, w = 11.0 cm, and L = 1.10 m. (v)

Explanation / Answer

magnetic field at point due to wire , B = uo*I/(2*pi*r)

magnetic flux through length L and width dr = dphi = B*A

dphi = uo*I*L*dr/(2*pi*r)

total magnetic flux = integration dphi

total magnetic flux = (uo*I*L/(2pi))*(lnr) from r = h to r = h+w

total magnetic flux = (uo*I*L/(2pi))*ln((h+w)/h)

total magnetic flux , phi = (uo*(a+bt)*L/(2pi))*ln((h+w)/h)

emf = rate of change in flux = (d/dt)*phi

emf = (uo*b*L/(2pi))*ln((h+w)/h)

emf = (4*pi*10^-7*20*1.1/(2*pi))*ln((0.01+0.11)/0.01)

emf = 1.1*10^-5 V <<<<<----answer

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