Electric field outside of charged sphere

In summary, for a sphere with a radius R and a charge Q distributed equally over the surface, the electric field at a point X inside the sphere is 0 if the distance r from X to the center of the sphere is less than the radius R. However, if the distance r is greater than R, the electric field is not 0 and can be denoted as w. This is also true if all the charge is concentrated at point X. In the case of non-uniformly distributed charge on the sphere, the electric field at point X may not be 0, but it can be assumed to be w if the sphere is conducting. To accurately solve electrostatic problems, one must take into account boundary conditions and the conductivity
  • #1
Imago23
1
0
Case 1. You have a sphere with Radius R and middle point X with the charge Q. The charge is equally distributed over the sphere.
for E(X,r) = 0 for r_1 < R, E inside the sphere is 0.
If r_2 > R then E ≠ 0 ; but let's say E(X,r_2) := w

If you put all the charge of the sphere into X then, it would still be E(X,r_2) = w
Why is that so? I could imagine that, if you had r_1 << R, but I found it first without the special case that R a lot larger than r_1
Where can I get information about that?

Case 2. Now the charge is no longer equally distributed over the sphere. Then E(X,r_1) is no longer 0. But what happens with E(X, r_2) ?
My guess is, that E = w, because in case 1 it didn't matter, if you viewed the sphere as a sphere or as a point. However I can't say for sure.

Can someone please help me?
 
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  • #2
You have to solve the electrostatic problems including the boundary conditions (at the surface, tangential components of the electric field must be continuous while normal components can jump if there is a surface charge).

Further you need to know, whether the sphere is conducting or not. This can, however only be the case for the two scenarios in case 1. Then you have the condition that the tangential components of the E-field must not only be continuous but also vanish along the surface, because statics demands that there must not be currents.
 

1. What is the formula for calculating the electric field outside of a charged sphere?

The formula for calculating the electric field outside of a charged sphere is E = kQ/r2, where E is the electric field, k is the Coulomb's constant, Q is the charge of the sphere, and r is the distance from the center of the sphere.

2. How does the electric field outside of a charged sphere differ from the electric field inside the sphere?

The electric field inside a charged sphere is zero because the electric charges are evenly distributed throughout the sphere, canceling out each other's electric fields. Outside the sphere, the electric field exists and decreases with distance from the sphere's center.

3. Does the electric field outside of a charged sphere depend on the type of material the sphere is made of?

No, the electric field outside of a charged sphere does not depend on the type of material the sphere is made of. It only depends on the charge of the sphere and the distance from its center.

4. How does the electric field outside of a charged sphere change as the distance from the sphere increases?

The electric field outside of a charged sphere decreases as the distance from the sphere increases. This is because the electric field is inversely proportional to the square of the distance from the center of the sphere.

5. Can the electric field outside of a charged sphere have a negative value?

Yes, the electric field outside of a charged sphere can have a negative value. This indicates that the electric field is directed towards the sphere, which can occur if the sphere has a negative charge.

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