Finding Distance Above Long Straight Wire Carrying Current

[brunie]

A long straight wire lies on a horizontal table and carries a current of 2.00 µA. In a vacuum, a proton moves parallel to the wire (opposite the current) with a constant speed of 1.90E4 m/s at a distance d above the wire. Determine the value of d. You may ignore the magnetic field due to the Earth.

ok so we have
0.000002 A
19000 m/s proton with mass and charge

the only problem i have is trying to understand what is going on in the problem and what needs to be balanced... once i understand what needs to be equated the physics behind it becomes more apparent... can anyone give me a brief explanation of what needs to be understood to solve this?

 

[Päällikkö]

The current in the wire creates a magnetic field around the wire as predicted by Ampère's law. There are two forces acting on the proton: Lorentz force (a charged particle in an electromagnetic field) and gravity.

 

[m2003]

Sure, let's break down the problem step by step. The first thing we need to understand is the concept of magnetic fields. When a current flows through a wire, it generates a magnetic field around it. This magnetic field can interact with other objects, such as the proton in this problem.

Next, we need to understand the motion of the proton. It is moving parallel to the wire, which means it is moving in the same direction as the current. This also means that the magnetic field will be perpendicular to its motion.

Now, we can use the right-hand rule to determine the direction of the magnetic field. If we point our thumb in the direction of the current, our fingers will curl in the direction of the magnetic field. In this case, the magnetic field will be pointing downwards, towards the table.

So, now we have a proton moving parallel to the wire and a magnetic field pointing downwards. This means that the proton will experience a force due to the interaction between its motion and the magnetic field.

The equation for this force is given by F = qvB, where q is the charge of the particle, v is its velocity, and B is the magnetic field. In this case, we know the charge of the proton (1.6 x 10^-19 C), its velocity (1.9 x 10^4 m/s), and the current in the wire (2.00 µA = 2.00 x 10^-6 A). We can also calculate the magnetic field using the formula B = μ0I/2πd, where μ0 is the permeability of free space (4π x 10^-7 Tm/A) and d is the distance from the wire.

Now, we have all the information we need to solve for the distance d. We can set the force due to the magnetic field equal to the force needed to keep the proton at a constant speed (since it is moving at a constant speed, we know that the net force on it is zero). This gives us the equation:

qvB = mv^2/d

Solving for d, we get:

d = mv/ qB

Plugging in the values we know, we get:

d = (1.6 x 10^-19 C)(1.9 x 10^4 m/s)/(2.00 x 10^-6 A)(4π x 10^-7 Tm/A)

Simplifying,