Insulating spherical shell prob

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A small, insulating, spherical shell with inner radius a and outer radius b is concentric with a larger insulating spherical shell with inner radius c and outer radius d. The inner shell has total charge +q distributed uniformly over its volume, and the outer shell has charge -q distributed uniformly over its volume.

How would i calculate the magnitude of the electric field for a < radius < b?

Would this forumla be correct?

q/(4*pi*Epsilon 0*(b-a)^2)

 

[Tide]

Why would you expect the electric field to be constant in the intermediate region?

 

[quicknote]

I would first like to clarify that the formula provided is not entirely correct. The correct formula for calculating the magnitude of the electric field at a distance r from the center of the shell is q/(4*pi*Epsilon 0*r^2), where q is the total charge on the shell and Epsilon 0 is the permittivity of free space.

To answer the question of how to calculate the electric field for a distance between the inner and outer radii of the inner shell, a < r < b, we can use the concept of superposition. This means that we can calculate the electric field at a point by considering the individual contributions from the charges on each shell separately.

In this case, the electric field at a point within the inner shell (a < r < b) will be the sum of the electric field contributions from the positive charges on the inner shell and the negative charges on the outer shell. We can use the formula mentioned earlier to calculate the electric field from each shell, and then add them together to get the total electric field at that point.

I would also like to mention that the electric field inside a conducting shell is always zero, so the electric field at a point within the inner shell will be zero for r < a.

In summary, to calculate the electric field at a point within the inner shell (a < r < b), we can use the concept of superposition and add the contributions from the charges on each shell separately. The correct formula for calculating the electric field at a distance r from the center of the shell is q/(4*pi*Epsilon 0*r^2).