Why is the electric field inside a conducting hollow/filled sphere zero?

In summary, the electric field inside a conducting hollow or filled sphere is zero due to the redistribution of charges on the surface of the conductor in response to external electric fields. This redistribution creates an opposing electric field that cancels any internal field, a consequence of electrostatic equilibrium. Additionally, any excess charge resides on the outer surface of the conductor, ensuring that the electric field within the material and the hollow region is null.
  • #1
aryan kumar pandey
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Homework Statement
a electric charge emits electric field lines radially. A charged conducting hollow/filled spheres have ellectric charges on its surface. How is the electric field inside the hollow/filled sphere zero?
Relevant Equations
E = kq/r^2
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  • #2
Start with the filled conducting solid. The stationary electric field inside any such conductor is zero because if it wasn't then that non-zero field would drive an electric current according to ##\vec J = \sigma \vec E##, where ##\sigma## is the conductance. In particular, this means that any charge on the conducting filled sphere is located on the surface because according to Gauss' law ##\rho \propto \nabla \cdot \vec E = 0## inside the conductor.

Now we know that any charge on the conducting filled sphere will arrange itself on the surface such that the internal field is zero. This charge configuration is also possible on the hollow sphere and will be the lowest energy configuration also in that case. Hence, also on the hollow sphere, the charge configuration on the surface will be such that the field inside is zero.
 
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  • #3
Hello and :welcome: !

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This picture is not correct if you mean that the electric field lines start at the center. They start at the positive charges. The positive charges evenly distribute themselves on the outside surface of the conducting spherical shell: if they were not evenly distributed, there would be a potential difference and the charges would move until there was no potential difference any more.

Inside the spherical shell the electric field contributions from the charges on the surface cancel. It would be a good exercise to actually do the integral and see this happen.

The conducting shell is an equipotential surface where the electric potential is constant; the electric field is the derivative and therefore it is zero.

See here

If you have already learned about Gauss' theorem the math becomes easier.

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FAQ: Why is the electric field inside a conducting hollow/filled sphere zero?

1. Why is the electric field inside a conducting hollow sphere zero?

The electric field inside a conducting hollow sphere is zero due to the properties of conductors in electrostatic equilibrium. When a conductor is charged, the charges redistribute themselves on the surface of the conductor. Inside the hollow region, the electric field cancels out because the charges on the surface create an opposing field that results in a net electric field of zero.

2. What happens to the electric field when a charge is placed inside a conducting hollow sphere?

When a charge is placed inside a conducting hollow sphere, it induces a charge on the inner surface of the sphere. This induced charge creates an electric field that exactly cancels the field produced by the charge within the hollow region. As a result, the electric field inside the conducting material and in the hollow space remains zero.

3. Does the size or shape of the conductor affect the electric field inside a hollow sphere?

No, the size or shape of the conductor does not affect the electric field inside a hollow sphere. As long as the conductor is in electrostatic equilibrium, the electric field inside the hollow region will always be zero, regardless of the sphere's dimensions or surface shape.

4. Is the electric field inside a solid conducting sphere also zero?

Yes, the electric field inside a solid conducting sphere is also zero. Similar to a hollow sphere, charges in a solid conductor redistribute themselves on the surface, leading to a cancellation of electric fields within the bulk of the conductor. Therefore, both inside a hollow and a solid conducting sphere, the electric field remains zero.

5. How does Gauss's law explain the zero electric field inside a conducting hollow sphere?

Gauss's law states that the electric flux through a closed surface is proportional to the charge enclosed within that surface. For a Gaussian surface placed inside a conducting hollow sphere, there is no charge enclosed (since the charge resides on the surface). Consequently, the electric flux is zero, which implies that the electric field inside the hollow region must also be zero.

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