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

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To determine the distance a proton must be from a current-carrying wire, the magnetic field created by the wire and the magnetic force acting on the proton must be analyzed. The current in the wire is 1.2x10^-6 A, and the proton moves parallel to the wire at a speed of 2.3x10^4 m/s. The key point is that since the proton is moving with constant velocity, the net force acting on it must be zero, implying that the magnetic force equals the gravitational force. The discussion revolves around applying Ampere's law and the Biot-Savart law to find the appropriate distance above the wire. Ultimately, the relationship between the forces leads to the determination of the required distance, d.
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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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Hint: Since the proton moves with constant velocity, what must the net force be on it?
 
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?
 
feelau said:
well net force should be zero but then would it mean F(magnetic)= mg
You got it.
 
oh thanks very much
 

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