Electric field inside charged conducting sphere?

In summary, the conversation discusses the concept of electrostatic equilibrium and how the electric field is zero at any point inside a sphere due to opposite point charges cancelling each other out. However, for points off-center, there may be a net field due to the distribution of point charges on the sphere's surface. This can be explained through a brute-force calculation or by using Gauss' Law. The conversation also mentions that this concept is covered in most E&M textbooks.
  • #1
mohamed el teir
88
1
i know it s zero because of the electrostatic equilibrium, but in terms of point charges : from the charge distribution on the sphere surface if we consider 2 point charges opposite to each other in direction : it s logical that at the point in the mid distance between them the electric field will be zero : (kq1/r1^2)=(kq2/r2^2) where q1=q2 and r1=r2, but if we consider a point closer to a point charge than the other charge : q1=q2 also but r1 not equal r2, therefore it s logical that there will be net field at this point, but there is no field at any point inside the sphere, so what is the solution of this contradictory ?
 
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  • #2
It's not just about those two point charges.
A brute-force calculation might help... after which one might have more appreciation for Gauss' Law.
 
  • #3
Very very crudely (I hate to do this) it's because for a point off-centre there are more point charges on the sphere further away than there are closer - the effect balances out exactly when you add them all up. Surely any E&M textbook shows how to do the integration.
 
  • #4
DaPi said:
Very very crudely (I hate to do this) it's because for a point off-centre there are more point charges on the sphere further away than there are closer - the effect balances out exactly when you add them all up. Surely any E&M textbook shows how to do the integration.
nailed it ! thanks man ...
 

1. What is an electric field inside a charged conducting sphere?

The electric field inside a charged conducting sphere is a vector quantity that represents the force per unit charge experienced by a test charge placed inside the sphere. It is created by the presence of the charged particles (usually electrons) within the sphere, which are free to move and distribute themselves evenly on the surface of the sphere.

2. How is the electric field inside a charged conducting sphere calculated?

The electric field inside a charged conducting sphere can be calculated using the formula E = Q/(4πεr^2), where E is the electric field, Q is the charge of the sphere, ε is the permittivity of the medium surrounding the sphere, and r is the distance from the center of the sphere.

3. Is the electric field inside a charged conducting sphere constant?

Yes, the electric field inside a charged conducting sphere is constant at all points. This is because the charge is distributed evenly on the surface of the sphere, resulting in a uniform electric field inside the sphere.

4. How does the electric field inside a charged conducting sphere vary with the distance from the center?

The electric field inside a charged conducting sphere varies inversely with the square of the distance from the center. This means that as the distance from the center increases, the electric field decreases. This relationship is described by the formula E = Q/(4πεr^2).

5. Can the electric field inside a charged conducting sphere be zero?

Yes, the electric field inside a charged conducting sphere can be zero if the net charge of the sphere is zero. In this case, the charges inside the sphere will distribute themselves in such a way that the electric field inside the sphere is canceled out. However, this is a rare occurrence and the electric field inside a charged conducting sphere is usually non-zero.

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