A long cylindrical conductor of radius a has two cylindrical cavities of diamete
ID: 2262834 • Letter: A
Question
A long cylindrical conductor of radius a has two cylindrical cavities of diameter a through its entire length, as shown in cross-section in the figure below. A current I is directed out of the computer screen and is uniform through a cross section of the conductor.
(a) Provide an equation that describes the magnitude of the magnetic field in terms of
A long cylindrical conductor of radius a has two cylindrical cavities of diameter a through its entire length, as shown in cross-section in the figure below. A current I is directed out of the computer screen and is uniform through a cross section of the conductor. Provide an equation that describes the magnitude of the magnetic field in terms of mu 0, I, r, and a at point P1. Provide an equation that describes the magnitude of the magnetic field in terms of mu 0, I, r, and a at point P2.Explanation / Answer
The cavity in the wire can be considered as two opposite and equal currents. Therefore we have a solid wire with current out of the screen (B1) and two smaller ones inside it with current going inside the screen(B2 & B3).
J = Current density = I/pi*a^2-pi* a^2/2 = 2*I/pi * a^2
B =
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