Wire with Current and electric field

[emtilt]

Wire with Current and associated fields - Urgent help needed

Homework Statement

A long wire of circular cross section with radius a carries a steady current i. Let the coordinate z denote position along the wire, $$\phi$$ denot orientation around the wire, and r denote perpendicular distance to the wire.
a)Assume a constant current density on the wire. Find an expression for the magnetic field inside and outside the wire.

b)A long 18-gauge copper wire has a diameter of 0.0403in. If the current in the wire is i=1A, what is the electric field required to drive the current in this wire?

c) What is the largest magnetic field within the wire? What is the ratio of the magnetic force to the electric force on an electron moving with the current at the position of strongest magnetic field?


I got part A easily enough. But, I have no idea what to do on part b. I couldn't get anywhere even after looking in my textbook, so I'm even wondering if maybe there was an error in the problem and the teacher left something out. Is there a way to do this that I am missing? For part c, I believe the magnetic field is strongest at the surface, but I have no idea how to get that ratio. The only thing I can think of is to write $$F_B=qv\mu_0 i/2\pi a$$ and $$F_E=q\rho j$$

 

[emtilt]

Can anyone help with this? I forgot to mention that I need help somewhat urgently, before tomorrow. I've been staring at this for quite some time and have made no progress.

 

[ogb p]

/2\pi r.

I would first like to commend you for reaching out for help when you were stuck. It shows that you are taking your work seriously and are willing to put in the effort to understand the material.

Now, let's tackle the problem at hand. Part A asks you to find an expression for the magnetic field inside and outside the wire. This can be done using Ampere's law, which states that the line integral of the magnetic field around a closed loop is equal to the current enclosed by that loop multiplied by the permeability of free space. In this case, the closed loop would be a circle of radius r, centered at the wire, and the current enclosed would be the current i. Using this information, you should be able to find the magnetic field inside and outside the wire.

For part B, the question is asking for the electric field required to drive a current of 1A through a wire with a diameter of 0.0403in. This can be calculated using Ohm's law, which states that the electric field is equal to the current divided by the resistance. The resistance can be calculated using the formula R = ρL/A, where ρ is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area of the wire.

For part C, you are correct in thinking that the magnetic field is strongest at the surface of the wire. To find the ratio of the magnetic force to the electric force on an electron moving with the current at the position of strongest magnetic field, you can use the formula F_B/F_E = v/μ_0ρ, where v is the velocity of the electron, μ_0 is the permeability of free space, and ρ is the resistivity of copper. This will give you the ratio at any point along the wire, and you can then find the maximum value at the surface.

I hope this helps you in solving the problem. If you are still having trouble, I would suggest reaching out to your teacher or a tutor for further clarification. Keep up the good work!