Calculating Current Through a Cylindrical Conductor

In summary, the current through the cross-section of a cylindrical conductor with radius a and placed along the z-axis can be found by integrating the current density given as it crosses the circle of radius a defined by the cylinder of the wire. It is easiest to switch to cylindrical coordinates for this integration.
  • #1
DODGEVIPER13
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Homework Statement


The current density in a cylindrical conductor of radius a placed along the z-axis is J=10e^-(1-ρ/a)Uz
Find the current through the cross-section of the conductor.

Homework Equations


I=JA
A=(pi)a^2

The Attempt at a Solution


So far I have this I=10e^-(1-ρ/a)Uz((pi)a^2) which I assume I am to integrate but what should I integrate with respect too and what should the limits be I am guessing from 0 to a?
 
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  • #2
You integrate the flow normal to the cross section through which it is flowing.
 
  • #3
So that would be along the x or y?
 
  • #4
The normal is the perpendicular vector right?
 
  • #5
Yes, the normal is perpendicular to the surface.
 
  • #6
ok so a normal vector equals to Uz/Uz (where the bottom Uz is the length of Uz it is in between those two absolute value mark things). Do you have any more hints on how to set this up
 
  • #7
Your problem states that the current is flowing along the axis Uz, hence it is perpendicular to the cross section formed by the x-y plane.

So you just have to integrate the density given as it crosses the circle of radius a defined by the cylinder of the wire. Since the axis passes along the center of the wire it would be easiest to switch to cylindrical coordinates for this integration.
 
  • #8
∫JdS=Ienc where dS=ρd(phi)dρ in cylindrical right?
 

1. What is current through the conductor?

Current through the conductor refers to the flow of electric charge through a material, such as a wire or a circuit. It is measured in amperes (A) and is the rate at which electric charge passes through a given point in a circuit.

2. How is current through the conductor related to voltage?

According to Ohm's Law, current through a conductor is directly proportional to the voltage applied. This means that as the voltage increases, the current also increases, and vice versa. The relationship between current and voltage is represented by the equation I = V/R, where I is current, V is voltage, and R is resistance.

3. What factors affect the amount of current through a conductor?

The amount of current through a conductor is affected by three main factors: voltage, resistance, and the type of material the conductor is made of. Higher voltage and lower resistance will result in a greater current flow, while materials with high conductivity, such as copper, will allow for more current to pass through.

4. How is current through a conductor measured?

Current through a conductor can be measured using a device called an ammeter. The ammeter is connected in series with the conductor and measures the amount of current passing through it. It is important to note that the ammeter should have a very low resistance in order to not affect the current flow in the circuit.

5. What are some practical applications of understanding current through a conductor?

Understanding current through a conductor is essential in many fields, including electrical engineering, physics, and electronics. It allows for the design and operation of various electrical systems, such as power grids, electronic devices, and circuits. It also helps in troubleshooting and diagnosing issues in these systems.

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