Determining current and drift speed

In summary, the problem is asking for the current and electron drift speed in a 2.0mm-diameter segment of two wires made of the same material. Using the equations I = J/A and J = n*e*v_d, where n is the density of the conductor and v_d is drift velocity, the density of the conductor was found to be 2*10^28 m^-3. It was also determined that I_2 = 20000v_{d_2}. After realizing that I_2 = I_1, the problem was solved.
  • #1
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[SOLVED] Determining current and drift speed

Homework Statement



http://img162.imageshack.us/img162/145/problemrg5.jpg

The two wires in the above figure are made of the same material. What are the current and the electron drift speed in the 2.0mm-diameter segment of the wire.

Homework Equations



I = J/A; J = n*e*v_d where n is the density of the conductor in m^-3 and v_d is drift velocity.

The Attempt at a Solution

I was able to find the density of the conductor:

[tex]n = \frac{I_{1}}{(Aev_{d_1})} = 2*10^{28}[/tex]

Also, I reached to this relationship between [tex]I_2[/tex] and [tex]v_{d_2}[/tex]:

[tex]I_{2} = 20000v_{d_2}[/tex]

What to do next? Appreciate any pointers, and thanks in advance.
 
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  • #2
Ah, again, I_2 = I_1. *smacks head* This solves the problem.
 
  • #3

To determine the current and electron drift speed in the 2.0mm-diameter segment of the wire, we can use the equations provided in the problem. First, we can use the equation I = J/A, where I is the current, J is the current density, and A is the cross-sectional area of the wire. We know that the two wires have the same material and the same diameter, so we can assume they have the same cross-sectional area. Therefore, we can set the two current densities equal to each other:

J_{1} = J_{2}

Next, we can use the equation J = n*e*v_d, where n is the density of the conductor, e is the charge of an electron, and v_d is the drift velocity. We can substitute this equation into our previous equation to get:

n_{1}*e*v_{d_1} = n_{2}*e*v_{d_2}

Since we know the density of the conductor for wire 1 (n_{1}) and we have a relationship between the current and drift velocity for wire 2 (I_{2} = 20000v_{d_2}), we can solve for v_{d_2}:

v_{d_2} = \frac{I_{2}}{20000}

Finally, we can use the equation I = J/A to solve for the current in the 2.0mm-diameter segment of the wire:

I_{2} = J_{2}*A = n_{2}*e*v_{d_2}*A

Substituting in our values, we get:

I_{2} = (2*10^{28}*e*\frac{I_{2}}{20000})*(3.14*10^{-6}) = 0.628*I_{2}

Solving for I_{2}, we get:

I_{2} = 1.59*10^{-6} A

Therefore, the current in the 2.0mm-diameter segment of the wire is 1.59*10^{-6} A and the electron drift speed is 1.59*10^{-6}/20000 = 7.95*10^{-11} m/s.
 

Related to Determining current and drift speed

1. What is current and drift speed?

Current and drift speed refer to the rate at which an object moves or is carried by a current, such as a river or ocean current. This can also refer to the speed at which particles or molecules move in a fluid, such as air or water.

2. How is current and drift speed measured?

Current and drift speed can be measured using instruments such as current meters or doppler current profilers, which measure the velocity of the water or fluid. Scientists can also use GPS and tracking devices to measure the movement of objects carried by the current.

3. What factors affect current and drift speed?

Current and drift speed can be affected by a variety of factors, including the strength and direction of the current, the shape and size of the object being carried, and the viscosity of the fluid. Other factors such as wind and temperature can also impact current and drift speed.

4. Why is it important to determine current and drift speed?

Understanding current and drift speed is important in a variety of fields, including oceanography, meteorology, and environmental science. It allows scientists to track the movement of pollutants, predict weather patterns, and study the behavior of marine animals, among other uses.

5. How do scientists use current and drift speed in their research?

Scientists use current and drift speed data in a variety of ways, such as creating maps and models to study ocean currents and predict their impact on climate. They also use this data to track the movement of marine animals, study the dispersal of pollutants, and make predictions about weather patterns and ocean conditions.

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