Tangential component of ElectroStatic Field

[abhs94]

There is the problem which i haven't been able to understand:

"Show that the tangential component of an electric field is continuous from one side of a conductor to the other"

What exactly is asked and how to prove it?

Thanks!

 

[McLaren Rulez]

Well, I'm not sure what its asking for exactly but the tangential component of the e-field in a conductor must be zero. If not, the electrons in the conductor rearrange themselves to make it zero. The fact that its zero everywhere means that it is continuous obviously. But perhaps they want a proof of this fact in some way which proves continuity without showing that its zero everywhere?

 

[Hassan2]

There is the problem which i haven't been able to understand:

"Show that the tangential component of an electric field is continuous from one side of a conductor to the other"

What exactly is asked and how to prove it?

Thanks!

Hi abhs94,

see this http://farside.ph.utexas.edu/teaching/em/lectures/node59.html

The continuity of tangential component of an electrostatic field is true for the boundary of any two materials. In a special case when one side of the boundary is conductor, on both sides, the tangential component is zero ( and of course still continuous ).

 

[abhs94]

Thanks a lot for that!

 

[sardar]

The tangential component of an electric field refers to the component of the field that is parallel to the surface of a conductor. In order to prove that this component is continuous from one side of a conductor to the other, we need to show that there is no abrupt change or discontinuity in the tangential electric field as we move from one side of the conductor to the other.

To do this, we can use the fact that at the surface of a conductor, the electric field is always perpendicular to the surface. This is known as the boundary condition for electric fields at the surface of a conductor. This means that at any point on the surface of a conductor, the tangential component of the electric field is zero.

Now, let's consider a point just outside the conductor, very close to its surface. At this point, the electric field will have both a normal component (perpendicular to the surface) and a tangential component (parallel to the surface). As we move closer to the surface, the normal component will decrease due to the boundary condition, but the tangential component will remain the same.

If we now consider a point just inside the conductor, again very close to its surface, the electric field will have a normal component (perpendicular to the surface) and a tangential component (parallel to the surface). However, since we are now inside the conductor, both components of the electric field will be smaller than they were at the point just outside the conductor. However, the ratio between the tangential and normal components will remain the same.

This shows that as we move from one side of the conductor to the other, the tangential component of the electric field remains continuous. Any change in the normal component is accompanied by a corresponding change in the tangential component, maintaining the same ratio between the two. This proves that the tangential component of the electric field is continuous from one side of the conductor to the other.