Figure P31.20 shows four current-carrying wires that are perpendicular to the pa

Question

Figure P31.20 shows four current-carrying wires that are perpendicular to the page, where I_1 = 1.0 A, I_2 = 2.0 A, I_3 = 3.0 A, and I_4 = 4.0 A. Four Amperian loops are also shown. Find the current through each loop. A thin, infinite conducting sheet lies in the xy plane. It carries current per unit length J in the positive y direction. Find an expression for the magnitude of the magnetic field near the infinite sheet. A steady current I flows through a wire of radius a. The current density in the wire varies with r as J = kr, where k is a constant and r is the distance from the axis of wire. Find for the magnitudes of the magnetic field inside and outside the wire a function of r.

Explanation / Answer

given

i1 = 1 A ,

i2 = 2 A ,

i3 = 3 A ,

i4 = 4 A ,

through A , the current enclosed is = i1 = 1 A

through B , the current enclosed is = i1 - i2 = 1 - 2 = - 1 A

through C , the current enclosed is = - i2 = - 2 A

through D , the current enclosed is = i2 + i4 = 2 + 4 = 6 A

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