Electric field in a spherical shell

In summary, the problem involves a conducting spherical shell with a charge of +7 nC located at the center and an inner radius of 2 m and an outer radius of 4 m. The electric field at r = 1 m is -45 N/C in the radially outward direction, at r = 3 m it is 0 N/C, and at r = 5 m it is 0.719 N/C in the radially outward direction. The surface charge distribution on the outside surface of the shell can be found using Gauss' Law, where E = σ/epsilon0.
  • #1
yjk91
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Homework Statement


A -5-nC point charge is located at the center of a conducting spherical shell. The shell has an inner radius of 2 m, an outer radius of 4 m, and a charge of +7 nC. (Let the radially outward direction be positive.)
(a) What is the electric field at r = 1 m? (Indicate the direction with the sign of your answer.)




(b) What is the electric field at r = 3 m? (Indicate the direction with the sign of your answer.)


(c) What is the electric field at r = 5 m? (Indicate the direction with the sign of your answer.)



(d) What is the surface charge distribution, σ, on the outside surface of the shell? (Indicate the direction with the sign of your answer.)




The Attempt at a Solution



a) you get this by doing -5 * 10^-9 * 9 * 10^9 / (1) ^2 = -45 N/C


(b) 0 N/C

i' not sure of this i thin it's because it's on the middle. Middle meaning middle of 2 M and 4 M which is 3M
i would like a clear answer

(c) What is the electric field at r = 5 m? (Indicate the direction with the sign of your answer.)
Units are required for this answer. 0.719 N/C

this i have no idea.. i think there is a formula but not sure how the charge of 7nC affects the field

(d) What is the surface charge distribution, σ, on the outside surface of the shell? (Indicate the direction with the sign of your answer.)

i think you use E = σ/epsilon0
 
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  • #2
Do you know Gauss' Law?

ehild
 

Related to Electric field in a spherical shell

1. What is an electric field in a spherical shell?

An electric field in a spherical shell is a type of electric field that exists within a spherical shell, which is a hollow, three-dimensional shape with a uniform thickness. This type of electric field arises due to the presence of electric charges on the surface of the spherical shell.

2. How is the electric field calculated in a spherical shell?

The electric field in a spherical shell can be calculated using the formula E = Q/4πεr^2, where Q is the total charge on the surface of the spherical shell, ε is the permittivity of the medium, and r is the distance from the center of the spherical shell to the point where the electric field is being calculated.

3. What is the direction of the electric field in a spherical shell?

The direction of the electric field in a spherical shell is radial, meaning it points away from or towards the center of the spherical shell. The direction is determined by the sign of the charge on the surface of the spherical shell.

4. How does the electric field change inside a spherical shell?

The electric field inside a spherical shell is zero. This is because the electric field is only present on the surface of the spherical shell, and there are no charges inside the shell to create an electric field.

5. Can the electric field in a spherical shell be non-uniform?

No, the electric field in a spherical shell is always uniform, meaning it has the same magnitude and direction at all points on its surface. This is because the spherical shape of the shell results in the distribution of charges being symmetrical, leading to a uniform electric field.

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