Why Is the Electric Field Not Zero Inside the Spherical Cavity?

[SupremeV]

Homework Statement

A spherical cavity of radius 4.50 cm is at the center of a metal sphere of radius 18.0 cm. A point charge Q = 6.40 µC rests at the very center of the cavity, whereas the metal conductor carries no net charge. Determine the electric field at the following points.
(a) 2.0 cm from the center of the cavity

Homework Equations

integral of ( E * dA ) = (1/Epsilon o) * Q enc
E = k q / r2

The Attempt at a Solution

The answer, is suppose to 1.44e8, and has a very straightforward use of E = k q / r2.

My question is why isn't the electric field 0 at 2.0 cm from the center at the cavity. Isn't that inside the static metal conductor, hence must be 0.

Thanks all!

 

[Andrew Mason]

Homework Statement

A spherical cavity of radius 4.50 cm is at the center of a metal sphere of radius 18.0 cm. A point charge Q = 6.40 µC rests at the very center of the cavity, whereas the metal conductor carries no net charge. Determine the electric field at the following points.
(a) 2.0 cm from the center of the cavity

Homework Equations

integral of ( E * dA ) = (1/Epsilon o) * Q enc
E = k q / r2

The Attempt at a Solution

The answer, is suppose to 1.44e8, and has a very straightforward use of E = k q / r2.

My question is why isn't the electric field 0 at 2.0 cm from the center at the cavity. Isn't that inside the static metal conductor, hence must be 0.

The short answer is: because Gauss' law would be violated if the field was 0. For a concentric Gaussian shell of radius 2 cm, the enclosed charge is not 0. So the field at the surface of that shell cannot be 0.

You may be confusing a situation in which you are to determine the field inside a charged sphere, with no charge inside the spherical cavity. In that case, there would be no enclosed charge (all the charge would be outside a Gaussian sphere of radius 2 cm) so the field would be 0.

AM

 

[cupid.callin]

Hi SupremeV

(Have an epsilon and integral: ε, ∫ and try using X² and X₂ button just above the reply box --- ©Tiny-Tim)

Field is only zero inside the material of the conductor ... not the hollow space

In this case ... the two surfaces(inner and outer) of hollow sphere will get come charge so as to balance the electric field due to central charge ... in in fact this property of conductors (and gauss law) is used to find this charge.

 

[SupremeV]

Thank you! I appreciate the help!

 

[rwisz]

The electric field inside a conductor is indeed zero, but in this case, the point charge Q inside the cavity creates an electric field that extends outside of the conductor. This electric field is not affected by the presence of the conductor and can be calculated using Gauss's Law. The electric field at a distance r from the center of the cavity is given by E = kQ/r^2, where k is the Coulomb's constant and Q is the charge inside the cavity. Therefore, at a distance of 2.0 cm from the center of the cavity, the electric field would be 1.44 x 10^8 N/C. This is because the charge Q inside the cavity is still exerting its influence on the point 2.0 cm from the center, despite being inside the conductor.