Magnetic and electric field between current carrying coaxial cables

In summary, the question discusses two long concentric, cylindrical conductors with a potential difference and equal but opposite currents. An electron traveling between the conductors is not affected by the current, but the potential difference can be treated as a separate E field along the radial direction. Using Ampere's Law and the formula for E field between concentric cylinders, an expression for the velocity of the electron is derived.
  • #1
disillusion
7
0

Homework Statement



Two long concentric, cylindrical conductors of radii a and b (a<b), are maintained with a potential difference V and carry equal but opposite currents I.
An electron, with velocity u parallel to the axis, enters the evacuated region between the conductors and travels undeviated. Find an expression for |u|.

I am not sure I understood the question very well and would like to see what others make of the question.
Since the current is flowing so there would be an E field along the direction of the current, which would not affect the electron. Should I just treat the potential difference as a separate E field along the radial direction?

Homework Equations


[tex]\oint_{C} \textbf{B}\cdot \textbf{dl}=\mu_{0}\int di[/tex]
[tex]\oint_{S} \textbf{E}\cdot \textbf{dA} = \frac{Q}{\epsilon_{0}}[/tex]
[tex]\textbf{F}=q(\textbf{E} +\textbf{u}\times \textbf{B})[/tex]

The Attempt at a Solution


The B field is curling around the inner cylinder.
Using Ampere's Law,
[tex]B=\frac{\mu_{0}I}{2\pi r}[/tex]
for a<r<b
r = distance from centres of cylinders

E field (electrostatics) of concentric cylinders
[tex]E=\frac{Q}{2\pi\epsilon_{0}r}[/tex]
where Q is charge per unit length, assuming length>>r

Following from above
Capacitance
[tex]C=\frac{2\pi\epsilon_{0}}{log_{e}(\frac{b}{a})}[/tex] per unit length
so using Q=CV, get
[tex]E=\frac{V}{r log_{e}(\frac{b}{a})}[/tex]

now force F=q(E+u^B)
so
[tex]|\textbf{u}|=\frac{|\textbf{E}|}{|\textbf{B}|}[/tex]
and so
[tex]|\textbf{u}|=\frac{2\pi V}{\mu_{0}I log_{e}(\frac{b}{a})}[/tex]

would this look right?
 
Last edited:
Physics news on Phys.org
  • #2
Should I just treat the potential difference as a separate E field along the radial direction?

I would think so.

The result looks OK.
 
  • #3


I would say that your solution looks correct. Your approach of using Ampere's Law and the equations for electric fields between concentric cylinders is a good way to solve this problem. However, I would suggest double-checking your calculations and units to ensure accuracy. Additionally, it might be helpful to provide a more detailed explanation of your thought process and reasoning for each step in your solution. This can help others, who may be struggling with the same problem, to better understand the concepts and techniques involved. Overall, your solution appears to be a solid response to the given problem.
 

1. What is the relationship between magnetic and electric fields in current carrying coaxial cables?

The magnetic and electric fields in current carrying coaxial cables are directly related. The magnetic field is perpendicular to the direction of current flow, while the electric field is parallel to it. This creates a circular magnetic field around the cable, which in turn creates an electric field that is parallel to the cable's axis.

2. How does the distance between two coaxial cables affect their magnetic and electric fields?

The distance between two coaxial cables has a significant impact on their magnetic and electric fields. As the distance decreases, the magnetic field between the cables becomes stronger and the electric field becomes weaker. This is due to the fact that the magnetic field is inversely proportional to the distance, while the electric field is directly proportional to it.

3. Can the magnetic and electric fields between two coaxial cables cancel each other out?

Yes, it is possible for the magnetic and electric fields between two coaxial cables to cancel each other out. This occurs when the currents in the two cables are equal and flowing in opposite directions. In this case, the magnetic fields will cancel each other out, while the electric fields will add together, resulting in a net electric field of zero.

4. How do the currents in the two coaxial cables affect their magnetic and electric fields?

The currents in the two coaxial cables have a direct impact on their magnetic and electric fields. As the currents increase, both the magnetic and electric fields become stronger. This is because the strength of these fields is directly proportional to the current flowing through the cables.

5. Are there any safety concerns related to the magnetic and electric fields between current carrying coaxial cables?

Yes, there are potential safety concerns related to the magnetic and electric fields between current carrying coaxial cables. These fields can interfere with sensitive electronic equipment and can also pose a risk to individuals with pacemakers or other medical devices. It is important to follow proper safety protocols and regulations when installing and using these cables to minimize any potential risks.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
903
  • Introductory Physics Homework Help
Replies
26
Views
425
  • Introductory Physics Homework Help
Replies
16
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
192
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
8
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
988
  • Introductory Physics Homework Help
Replies
17
Views
279
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
993
Back
Top