Electric field inside conductor

In summary, a spherical conducting shell with a centrally-located point charge has an electric field present at radii (i) less than a, (ii) between a and b, and (iii) greater than b, but the field is zero inside the conductor (a < r < b) due to the presence of induced charges that cancel out the field from the central point charge.
  • #1
bigplanet401
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Homework Statement



A spherical conducting shell of inner radius a and outer radius b contains a centrally-located point charge +Q. Is an electric field present at radii (i) less than a, (ii) between a and b, and (iii) greater than b?

Homework Equations





The Attempt at a Solution



My textbook says the electric field inside a conductor (a<r<b here) is zero, but I can't understand why. In (i), the field is that due to the charge. In (iii), field lines emanate from the surface at right angles (because the induced charge is positive on the outer surface).

In (ii), it seems like the field should be non-zero because of the induced positive charge on the outer surface and the induced negative charge on the inner surface. Wouldn't this create an electric field directed radially inward from r=b to r=a? The textbook says it's zero.

Thanks for your help!
 
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  • #2
bigplanet401 said:

Homework Statement



A spherical conducting shell of inner radius a and outer radius b contains a centrally-located point charge +Q. Is an electric field present at radii (i) less than a, (ii) between a and b, and (iii) greater than b?

Homework Equations





The Attempt at a Solution



My textbook says the electric field inside a conductor (a<r<b here) is zero, but I can't understand why. In (i), the field is that due to the charge. In (iii), field lines emanate from the surface at right angles (because the induced charge is positive on the outer surface).

In (ii), it seems like the field should be non-zero because of the induced positive charge on the outer surface and the induced negative charge on the inner surface. Wouldn't this create an electric field directed radially inward from r=b to r=a? The textbook says it's zero.

Thanks for your help!

Yes, the induced negative charge on the inner surface and the induced positive charge on the outer surface create a radially inward electric field that is just enough to cancel the radially outward electric field from the central point charge in this region a < r < b.

The point of an ideal conductor is that it can be considered a sort of limitless source of free charge. So, the E-field from the central point charge pushes charges around inside the conductor until they are arranged in such as way as to cancel out the field. If the field were not canceled out, and there were still a NET electric field inside the conductor, then this net electric field would push around even MORE charges until the arrangement was such that the field inside the conductor was zero.
 

1. What is an electric field inside a conductor?

The electric field inside a conductor is a region where charged particles experience a force. In a conductor, the electric field is zero as the charges are free to move and redistribute themselves in such a way that the electric field cancels out.

2. Why is the electric field inside a conductor zero?

The electric field inside a conductor is zero because in a conductor, the charges are free to move and redistribute themselves in such a way that the electric field cancels out. This is known as electrostatic equilibrium.

3. Can the electric field inside a conductor ever be non-zero?

Yes, under certain conditions, the electric field inside a conductor can be non-zero. This can occur if the conductor is not in electrostatic equilibrium, or if there is an external electric field present that is strong enough to overcome the repulsive forces between the charges within the conductor.

4. How does the shape and size of a conductor affect the electric field inside?

The shape and size of a conductor can affect the electric field inside in two ways. Firstly, the larger the surface area of the conductor, the greater the number of charges that can reside on the surface, resulting in a stronger electric field inside. Secondly, the shape of the conductor can affect the distribution of charges and thus the resulting electric field inside.

5. How is the electric field inside a conductor related to the charge on the surface?

The electric field inside a conductor is directly proportional to the surface charge density, which is the amount of charge per unit area on the surface of the conductor. This means that the greater the charge on the surface, the stronger the electric field inside the conductor.

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