Solving Physics Assignment: Launching a Plastic Stirrer with Electricity

In summary, the electric force on the plastic stirrer is 4.57E-4 Newtons if the end closest to the wire is 2.0 cm away.
  • #1
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Homework Statement



Your physics assignment is to figure out a way to use electricity to launch a small 6.0-cm-long plastic drink stirrer. You decide that you'll charge the little plastic rod by rubbing it with fur, then hold it near a long, charged wire. When you let go, the electric force of the wire on the plastic rod will shoot it away. Suppose you can charge the plastic stirrer to 11.0 nC and that the linear charge density of the long wire is 1.0 *10^{ - 7C/m. What is the electric force on the plastic stirrer if the end closest to the wire is 2.0 cm away?


Homework Equations


force lawF=qE
Gauss's law [tex]\Phi_E = \int E*dA[/tex]


The Attempt at a Solution



Well before I can solve this, I need to know the electric field that is coming off of the wire. So I use Gauss's law to determine that. I can place a cylinder around the wire and find the surface area of the cylinder excluding the ends. So

[tex]\Phi_E = \int E*dA = 2(pi)RLE=Q/\epsilon_{o}[/tex]

Where 2(pi)RL is just the surface area of the wire. Moving the surface area to the other side you can solve for E.


[tex]E=Q/(\epsilon_{o}*2(pi)RL)[/tex]

Since we know the charge density of the wire. we can replace Q with L[tex]\lambda[/tex] since they equal each other. Plugging that in and simplifying gives you the new formula

[tex]E=\lambda/(\epsilon_{o}*2(pi)R)[/tex]

And all you need to know is the radius of the charges away from the wire. My problem is how do you figure out where to take this radius from? I don't think the stirrer can be treated like a point charge. Where do I go from here?
 
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  • #2
Integration. I don't think you have any other choice.
 
  • #3
ideasrule said:
Integration. I don't think you have any other choice.

So wait. Should I take the charge density of the stirrer multiplied by dL ([tex]\lambda dL[/tex]) and then replace R with (.02 +L)? Does that make any sense?
 
  • #4
I did out the problem and was able to get 4.57E-4 Newtons. Very happy that I was able to get this answer! I usually don't do integration like this to solve physics problems :).

Thanks for the help
 

What is the concept behind launching a plastic stirrer with electricity?

The concept behind launching a plastic stirrer with electricity is based on the principles of electromagnetism. When an electric current is passed through a wire, it creates a magnetic field. This magnetic field can interact with another magnetic field, such as the Earth's magnetic field, to create motion.

What materials are needed to launch a plastic stirrer with electricity?

To launch a plastic stirrer with electricity, you will need a plastic stirrer, a power source (such as a battery or a power supply), a piece of wire, and a strong magnet. You may also need a launch platform and a way to control the flow of electricity, such as a switch or a circuit.

How do you calculate the force needed to launch a plastic stirrer with electricity?

The force needed to launch a plastic stirrer with electricity can be calculated using the equation F = BIL, where F is the force, B is the magnetic field strength, I is the current, and L is the length of the wire. The current can be calculated using Ohm's law (I = V/R), where V is the voltage and R is the resistance of the wire. The magnetic field strength can be measured using a gaussmeter.

What are some safety precautions to consider when launching a plastic stirrer with electricity?

When launching a plastic stirrer with electricity, it is important to follow safety precautions to avoid any accidents or injuries. Some safety precautions to consider include using a low voltage power source, wearing protective gear such as gloves and safety glasses, keeping the wire and stirrer away from your face and body, and making sure the launch platform is stable and secure.

How can the launch distance of a plastic stirrer be increased with electricity?

The launch distance of a plastic stirrer can be increased by increasing the strength of the magnetic field, increasing the current, or increasing the length of the wire. However, it is important to note that there may be a limit to how far the stirrer can be launched, as factors such as air resistance and the weight of the stirrer can affect the distance. Experimentation and trial and error may be necessary to find the optimal launch distance.

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