The figure below shows a rectangular loop of wire with length a = 3.4 cm, width

Question

The figure below shows a rectangular loop of wire with length a = 3.4 cm, width b = 1.6 cm placed near an infinitely long wire carrying current i = 4.3 A. Which describes the magnetic field within the loop? a) It is uniform and directly into the page. b) It is nonuniform and directly into the page. c) It is uniform and directly out of the page. d) It is nonuniform and directly out of the page. What is the correct expression for the infinitesimal area element of the loop you should use to find the magnetic flux through the loop? a) dA = abdr b) dA = ab c) dA = adr d) dA = abrdr What is the flux when the loop is at a distance r from the wire? a) phi_ = mu_0 i/2 pi ln(r + 0.5b/r - 0.5b) b) phi_ = mu_0/2 pi R ab c) phi_ = mu_0/ln(r/) d) phi_h = mu_0/2 pi R ar As the loop moves away from the wire with the speed of 0.0022 m/s, the changing flux induces an emf around the loop. What is the magnitude and direction of the emf when r = 4.7 cm? a) 1.0 middot 10^-8 V, counterclockwise b) 4.8 middot 10^-10 V, counterclockwise c) 1.0 middot 10^-8 V clockwise d) 4.8 middot 10^-10 V, clockwise Now assume that instead of the rectangular loop a sphere of radius R is placed near the straight wire with its center at a distance d from the wire. What is the total magnetic flux passing through the sphere? a) phi_ = mu_0/b) phi_ = mu_0/2 pi r c) Phi_ = mu_0 d) phi_H = 0

Explanation / Answer

35)

OPTION (b)

(36)

dA = a*dr

OPTION(c)

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37)

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*a*dr/(2*pi*r)

total magnetic flux = integration dphi

total magnetic flux = (uo*i*a/(2pi))*(lnr2/r1) from r1 = r-b/2 to r2 = r+b/2

total magnetic flux = (uo*i*a/(2pi))*ln((r+0.5b)/(r-0.5b))

OPTION(a)

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emf = rate of change in flux = (d/dt)uo*i*a*dr/(2*pi*r)

emf = uo*i*a*v/(2*pi*r)

emf = (4*pi*10^-7*0.034*4.3*0.0022/(2*pi*0.047)

emf = 1.0*10^-9 V clock wise

option (c)<<<<<----answer

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option(d)

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