How Do You Determine the Distance a Proton Must Be from a Current-Carrying Wire?

In summary, a proton with a constant speed of 2.3x10^4 m/s moves parallel to a long straight wire carrying a current of 1.2x10^-6A on a horizontal table. To determine the value of d, we can use Ampere's Law and Biot Savart Law to calculate the magnetic field and then set it equal to the gravitational force on the proton. Since the proton is moving with constant velocity, the net force on it must be zero, leading to the equation F(magnetic) = mg. Solving for d, we can determine the distance above the wire at which the proton is moving.
  • #1
feelau
61
0

Homework Statement


So a long straight wire lies on a horizontal table and carries a current of 1.2x10^-6A. In a vacuum, a proton moves parallel to the wire(opposite the current) with a constant speed of 2.3x10^4 m/s at a distance d above the wire. Determine the value of d. You may ignore the magnetic field due to the Earth.

Homework Equations


ampere's law
F(magnetic field)=q(vxB)
Biot savart law?

The Attempt at a Solution


So what I did is have the magnetic field formula for a wire, I then substitute this into the magnetic force equation. But now I don't really know where to go from there. Please help. Thanks very much.
 
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  • #2
Hint: Since the proton moves with constant velocity, what must the net force be on it?
 
  • #3
well net force should be zero but then would it mean F(magnetic)= mg or I am not sure what it would be equal to?
 
  • #4
feelau said:
well net force should be zero but then would it mean F(magnetic)= mg
You got it.
 
  • #5
oh thanks very much
 

FAQ: How Do You Determine the Distance a Proton Must Be from a Current-Carrying Wire?

What is Ampere's Law and why is it important in physics?

Ampere's Law is a fundamental law in electromagnetism that relates the magnetic field around a closed loop to the electric current passing through that loop. It is important in physics because it allows us to calculate the magnetic field produced by a current, which is crucial in understanding the behavior of electric motors, generators, and other devices.

How do I apply Ampere's Law to solve a problem?

To apply Ampere's Law, you will need to have information about the current passing through a closed loop and the geometry of the loop. You can then use the equation B = μ0 * I * N / L, where B is the magnetic field, μ0 is the permeability of free space, I is the current, N is the number of turns in the loop, and L is the length of the loop. Plug in the known values and solve for B.

What are some common mistakes to avoid when using Ampere's Law?

One common mistake is forgetting to account for the direction of the current and the direction of the loop. Make sure to use the right-hand rule to determine the direction of the magnetic field and make sure it is consistent with the direction of the current. Another mistake is not using the correct units for the variables. Make sure to use SI units for all values.

Can Ampere's Law be used to calculate the magnetic field for any current-carrying loop?

No, Ampere's Law can only be used for simple, symmetrical loops where the magnetic field is constant along the entire loop. For more complex loops, you will need to use more advanced techniques, such as numerical integration.

How does Ampere's Law relate to Faraday's Law of Induction?

Ampere's Law and Faraday's Law of Induction are closely related and together they form the basis of electromagnetism. Ampere's Law deals with the creation of a magnetic field by an electric current, while Faraday's Law deals with the creation of an electric current by a changing magnetic field. They are both essential for understanding the behavior of electromagnetic systems.

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