Magnitude of the electric field in a copper wire.

• Pepjag
In summary, the conversation discusses a circuit with copper and Nichrome wires, and their properties such as radius, length, and electron mobility. The question asks for the magnitude of the electric field in the copper wire. The solution involves using equations for drift velocity, resistance, and current, as well as the known voltage of the battery.
Pepjag

Homework Statement

In the circuit shown, two thick copper wires connect a 1.5 V battery to a Nichrome wire. Each copper wire has radius R = 7 mm and is L = 18 cm long. Copper has 8.4 × 10^28 mobile electrons per cubic meter and an electron mobility of 4.4×10^−3 (m/s)/(V/m). The Nichrome wire is l = 5 cm long and has radius r = 3 mm. Nichrome has 9 × 10^28 mobile electrons/m3 and an electron mobility of 7 × 10^−5 (m/s)/(V/m). What is the magnitude of the electric field in the copper wire? Answer in units of N/C

Homework Equations

$\bar{v}$$_{thin}$=(A$_{thick}$/A$_{thin}$)$\bar{v}$$_{thick}$

$\bar{v}$ = uE

E=V/L

The Attempt at a Solution

I plug in my known values, but I have two unknowns, the electric fields. I'm not sure how to use these equations.

You also know other stuff: that ##2V_{Cu}+V_{Ni}=1.5V## for example.

You also know all kinds of physics about the drift velocity, resistance, current etc. to draw on.
http://en.wikipedia.org/wiki/Drift_velocity

I had figured it out for a while now but thanks anyway. I just had to use the electron current formula and the voltage loop formula (as you stated); Plug in numbers, solve for e-field and plug into the other equation.

Cool - hopefully someone else stuck on a similar problem will benefit from your question ;)

I would first acknowledge that this is a complex problem and requires multiple equations and assumptions to solve. I would also clarify any assumptions made, such as assuming the wires are perfect conductors and the circuit is in steady-state.

To solve for the magnitude of the electric field in the copper wire, we can use the equation E = V/L, where V is the voltage and L is the length of the wire. In this case, the voltage is given as 1.5 V and the length of each copper wire is 18 cm. However, we still need to determine the voltage drop across the copper wire.

To do this, we can use the equation \bar{v} = uE, where \bar{v} is the average velocity of the electrons, u is the electron mobility, and E is the electric field. We can assume that the electric field is the same throughout the copper wire, since it is a perfect conductor.

To find the average velocity of the electrons, we can use the equation \bar{v}_{thin}=(A_{thick}/A_{thin})\bar{v}_{thick}, where A_{thick} is the cross-sectional area of the thick copper wire and A_{thin} is the cross-sectional area of the thin copper wire. We can assume that the cross-sectional area of the thin copper wire is negligible compared to the thick wire, so we can simplify the equation to \bar{v}_{thin}=\bar{v}_{thick}.

Now, we can solve for the average velocity of the electrons in the thick copper wire by plugging in the known values for the number of mobile electrons per cubic meter and the electron mobility. Then, we can use this value to solve for the electric field using the equation \bar{v} = uE.

Once we have the electric field, we can use the equation E = V/L to calculate the magnitude of the electric field in the copper wire. This will give us our final answer in units of N/C.

Overall, the magnitude of the electric field in the copper wire will depend on the assumptions made and the values used in the equations. It is important to carefully consider all factors and assumptions when solving complex problems like this.

1. What is the magnitude of the electric field in a copper wire?

The magnitude of the electric field in a copper wire depends on various factors such as the current flowing through the wire, the distance from the wire, and the diameter of the wire. It can range from a few volts per meter to thousands of volts per meter.

2. How is the magnitude of the electric field in a copper wire calculated?

The magnitude of the electric field in a copper wire can be calculated by dividing the voltage by the distance between two points on the wire. It can also be calculated by multiplying the current by the resistance of the wire.

3. What is the unit of measurement for the magnitude of the electric field in a copper wire?

The unit of measurement for the magnitude of the electric field in a copper wire is volts per meter (V/m).

4. How does the magnitude of the electric field in a copper wire affect the flow of electricity?

The magnitude of the electric field in a copper wire affects the flow of electricity by determining the strength and direction of the force on the electrons. A stronger electric field will cause the electrons to move faster and with more force, resulting in a higher current.

5. Can the magnitude of the electric field in a copper wire be changed?

Yes, the magnitude of the electric field in a copper wire can be changed by altering the voltage, current, or distance from the wire. It can also be affected by changing the material or diameter of the wire.

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