Confused about the electric field at the surface of a conductor

In summary, the electric field at the surface of a conductor only has a normal component equal to ρ/ε, as determined by the gradient of the electric field. However, when considering a point P on the surface of the conductor, the normal component of the field is infinite due to the formula E=Kq/r. This is because the charges in the conductor respond to the small charge close to the conductor, affecting the total field. The charge in question is actually part of the conductor, and inside a conductor, the charges are infinitesimally small. Therefore, the field at point P can be obtained using the formula E=Kq/r, but it is important to consider what "q" represents in this equation,
  • #1
parsa7parsa
3
0
Hi
We know that the electric field at the surface of a conductor only have a normal component equal to ρ /ε (finite number).
But let’s consider the point P (at the surface of a conductor ) . Assume that there is a charge at an infinitesimal distance from the point p . we can obtain the field at the P by the fourmula (E=Kq/r) .obviously, E ~1/r. so the normal component of the field is infinite. Now if we add the field due to other charges, it will remain infinite. So where could I be possibly wrong?
 
Physics news on Phys.org
  • #2
We know that the electric field at the surface of a conductor only have a normal component equal to ρ /ε (finite number).
It's the gradient of the electric field that has that value.

The charges in the conductor will respond to the electric field of the small charge close to the conductor - affecting the way the total field comes out. How do they respond?

Note - at a very small distance from a point charge, the field is not infinite.
If the charge is actually at point P, then it is part of the conductor. Inside a conductor, the charges are infinitesimally small (in this model).
 
  • #3
parsa7parsa said:
we can obtain the field at the P by the fourmula (E=Kq/r)

You should ask yourself what exactly is "q" in that equation going to be for your capacitor with a given charge density (*cough*) ρ
 
  • #4
please note that the charge is <within> the conductor
 
  • #5


Hello, it is natural to feel confused about the electric field at the surface of a conductor as it can be a complex concept to understand. However, it is important to remember that the electric field at the surface of a conductor is always perpendicular to the surface and its magnitude is determined by the surface charge density (ρ) and the permittivity of the material (ε). This is known as the "boundary condition" for electric fields at the surface of a conductor.

In the scenario you have described, the point P is located on the surface of the conductor and therefore, the electric field at that point is determined by the charge distribution on the surface. The formula you have mentioned (E=Kq/r) is applicable for the electric field at a point due to a point charge, but it cannot be used to determine the electric field at the surface of a conductor.

Additionally, the electric field at a point due to a point charge becomes infinite as the distance (r) approaches zero. However, in the case of a conductor, the surface charge density (ρ) is distributed over a finite area and therefore, the electric field at the surface remains finite.

It is also important to note that the electric field at the surface of a conductor is affected by the presence of other charges in its vicinity. This is known as the "superposition principle" where the total electric field at a point is the sum of the individual electric fields due to each charge.

In conclusion, the electric field at the surface of a conductor is determined by the surface charge density and is affected by the presence of other charges. It is not appropriate to use the formula for electric field due to a point charge to determine the electric field at the surface of a conductor. I hope this helps to clarify any confusion you had. Keep exploring and learning about electric fields!
 

What is the electric field at the surface of a conductor?

The electric field at the surface of a conductor is the force per unit charge that would be exerted on a small positive test charge placed at that point. It is a measure of the strength and direction of the electric field lines at the surface of the conductor.

Why is the electric field at the surface of a conductor sometimes confusing?

The electric field at the surface of a conductor can be confusing because it is dependent on the charge distribution and shape of the conductor. It can also be affected by nearby charges or external electric fields, making it difficult to determine the exact value at a specific point.

Can the electric field at the surface of a conductor ever be zero?

Yes, the electric field at the surface of a conductor can be zero in certain cases. If the conductor is a perfect conductor, it will have no net charge on its surface and therefore no electric field at its surface. Additionally, if the conductor is shielded from external electric fields, the field at its surface will also be zero.

How does the electric field at the surface of a conductor relate to its charge?

The electric field at the surface of a conductor is directly proportional to the charge density of the conductor. This means that the more charge the conductor has, the stronger the electric field will be at its surface. It is also affected by the shape and distribution of the charge on the conductor's surface.

What happens to the electric field at the surface of a conductor when a charged object is brought near it?

The electric field at the surface of a conductor will be affected by the presence of a nearby charged object. If the object has the same charge as the conductor, the electric field at the surface will be repulsive, causing the surface charges to redistribute. If the object has the opposite charge, the electric field at the surface will be attractive, causing the charges to shift towards the side closest to the object.

Similar threads

Replies
3
Views
381
  • Electromagnetism
Replies
14
Views
1K
  • Electromagnetism
Replies
15
Views
1K
  • Electromagnetism
Replies
4
Views
856
  • Electromagnetism
Replies
3
Views
753
Replies
4
Views
941
Replies
44
Views
2K
Replies
2
Views
2K
Replies
9
Views
1K
Back
Top