ch29-p065 - 65. (a) The magnetic field at a point within...

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65. (a) The magnetic field at a point within the hole is the sum of the fields due to two current distributions. The first is that of the solid cylinder obtained by filling the hole and has a current density that is the same as that in the original cylinder (with the hole). The second is the solid cylinder that fills the hole. It has a current density with the same magnitude as that of the original cylinder but is in the opposite direction. If these two situations are superposed the total current in the region of the hole is zero. Now, a solid cylinder carrying current i which is uniformly distributed over a cross section, produces a magnetic field with magnitude B ir R = µ 0 2 2 π at a distance r from its axis, inside the cylinder. Here R is the radius of the cylinder. For the cylinder of this problem the current density is J i A i ab == π 22 c h , where A = π ( a 2 b 2 ) is the cross-sectional area of the cylinder with the hole. The current in the cylinder without the hole is IJ AJ a ia 1 2 2 = π
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ch29-p065 - 65. (a) The magnetic field at a point within...

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