# Easy Electrodynamics Question on Field Lines

• Kyle91
In summary, the electric field is perpendicular to any conducting surfaces in static situations, and this is true in general for changing electric or magnetic fields. The magnetic field lines at the surface of a conductor are tangential due to the div-free condition, but there are no other restrictions on their direction.
Kyle91

## Homework Statement

Explain why the electric field is perpendicular to any conducting surfaces in static situations. Is this true in general (i.e. even for changing electric or magnetic fields)? Are there similar conditions on the direction of a magnetic field at the surface of a conductor.

## The Attempt at a Solution

I know how to do the first bit regarding static electric fields, but I can't find anything online about changing electric fields.

Everything I do find says 'Always must be perpendicular', but their justification is that it wouldn't be static if it wasn't normal. Therefore I think it is possible to have non-perpendicular field lines at the surface provided the charges in the conductor aren't static.

I need some sort of justification for this (other than what I've said above) so if you could point me in the right direction it'd be greatly appreciated.

About the magnetic fields, from wikipedia -

"A magnetic field has no sources or sinks (Gauss's law for magnetism), so its field lines have no start or end: they can only form closed loops, or extend to infinity in both directions."​

Now the bit I'm not sure about, is it right to say that these magnetic field lines are perpendicular to the electric field lines near the surface of a conductor? In other words, they look exactly like equipotential lines. Take this (http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imgele/equiv3.gif) image for example, if I were to draw in mag field lines I could trace over the dots and put arrows in a clockwise direction, right?

I'm getting confused because I'm trying to apply the right hand rule and can't think of anything curling around a vector :S

Cheers

The magnetic field B at the surface of conductor is tangential only from the div-free condition of B, (draw a small cylinder across the surface and knowing B=0 inside the conductor tells you vertical B=0). Because they are div-free, their field line at the surface are closed loops. But there are no other restrictions on it. (They are of course perpendicular to E field, because E field is perpendicular to the surface)

## 1. What are field lines?

Field lines are imaginary lines used to represent the direction and strength of an electric or magnetic field. They are drawn as continuous curves that start at a positive charge or north pole and end at a negative charge or south pole.

## 2. How are field lines related to electric and magnetic fields?

Field lines are used to visually represent the electric and magnetic fields. The density and direction of the field lines indicate the strength and direction of the field at a particular point. The closer the field lines are together, the stronger the field is at that point.

## 3. Can field lines cross each other?

No, field lines cannot cross each other. This is because at the point where two field lines intersect, there would be two different directions for the field, which is physically impossible. Therefore, field lines always repel each other and never intersect.

## 4. How do field lines change near a charged object?

Field lines change near a charged object by becoming closer together as they approach the object and spreading out as they move away from it. This indicates the strength of the field, with a higher concentration of field lines indicating a stronger field.

## 5. What is the purpose of using field lines?

The purpose of using field lines is to visually represent the electric and magnetic fields. They provide a useful way to understand and analyze these fields, as well as predict the behavior of charged particles and magnets in these fields.

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