To find the total current in the conductor, we need to find the total cross-sectional area of the conductor and then multiply it by the average current density.
Since the conductor is cylindrical, the cross-sectional area of the conductor is simply equal to the area of the circle with a radius of 2 mm. The area of a circle is equal to πr^2, where r is the radius of the circle. So, in this case, the cross-sectional area of the conductor is equal to π(2 mm)^2 = 4π mm^2.
The average current density is equal to the total current density divided by the total cross-sectional area. In this case, the total current density is equal to 1 x 10^3 * e^(-400r), where r is the distance from the axis of the conductor. Since the conductor has a radius of 2 mm, we can plug in 2 mm for r to find the total current density at that point. This gives us 1 x 10^3 * e^(-400 * 2) = 7.49 x 10^-72.
Finally, to find the total current, we just need to multiply the average current density by the cross-sectional area of the conductor. So, in this case, the total current is equal to (7.49 x 10^-72) * (4π mm^2) = 2.996 x 10^-71 A. This is the total current flowing through the conductor.
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Answer:
Step-by-step explanation:
To find the total current in the conductor, we need to find the total cross-sectional area of the conductor and then multiply it by the average current density.
Since the conductor is cylindrical, the cross-sectional area of the conductor is simply equal to the area of the circle with a radius of 2 mm. The area of a circle is equal to πr^2, where r is the radius of the circle. So, in this case, the cross-sectional area of the conductor is equal to π(2 mm)^2 = 4π mm^2.
The average current density is equal to the total current density divided by the total cross-sectional area. In this case, the total current density is equal to 1 x 10^3 * e^(-400r), where r is the distance from the axis of the conductor. Since the conductor has a radius of 2 mm, we can plug in 2 mm for r to find the total current density at that point. This gives us 1 x 10^3 * e^(-400 * 2) = 7.49 x 10^-72.
Finally, to find the total current, we just need to multiply the average current density by the cross-sectional area of the conductor. So, in this case, the total current is equal to (7.49 x 10^-72) * (4π mm^2) = 2.996 x 10^-71 A. This is the total current flowing through the conductor.