Thick spherical shell Question.

[twinpair]

Homework Statement

A thick spherical shell with inner radius R and outer radius S has a uniform charge density d.(A) What is the total charge on the shell? Express your answer in terms of R, S, d, and π. (B) Express the electric field as a function of distance from the center of the sphere r, R, S, d, and the permitivity of free space p for each of the following regions: 0<r<R , R<r<S, S<r

Homework Equations

E = kQ/r2

V=(4/3)πr3

The Attempt at a Solution

(For part A)
Since its a thick shell the volume would be V = (4/3)π(S^3 - R^3)

and dV = Qenc => d=Q/V

so

d = 3Q/(4π(S^3 - R^3))

(For part B)
0<r<R
the electric field will be 0 because the electric field can't close on itself

R< r< S
E=kQenc/r2 = (4πkρ(r^3 - R^3))/3r^2

S<r
E = kQ/r2 because the sphere can be treated as a point charge and the electric field is symmetric on a sphere

Is this correct?

 

[nrqed]

Homework Statement

A thick spherical shell with inner radius R and outer radius S has a uniform charge density d.(A) What is the total charge on the shell? Express your answer in terms of R, S, d, and π. (B) Express the electric field as a function of distance from the center of the sphere r, R, S, d, and the permitivity of free space p for each of the following regions: 0<r<R , R<r<S, S<r

Homework Equations

E = kQ/r2

V=(4/3)πr3

The Attempt at a Solution

(For part A)
Since its a thick shell the volume would be V = (4/3)π(S^3 - R^3)

and dV = Qenc => d=Q/V

so

d = 3Q/(4π(S^3 - R^3))

(For part B)
0<r<R
the electric field will be 0 because the electric field can't close on itself

R< r< S
E=kQenc/r2 = (4πkρ(r^3 - R^3))/3r^2

S<r
E = kQ/r2 because the sphere can be treated as a point charge and the electric field is symmetric on a sphere

Is this correct?

Everything looks good. But note that for part A they want Q. And for the other problems, you must give the answer in terms of $d , R, S$

 

[twinpair]

So for part A would it be Q = dv --> Q = d * (4/3)π(S^3 - R^3)

And for other problems what does it mean to give the answer in terms of d,R,S

 

[nrqed]

So for part A would it be Q = dv --> Q = d * (4/3)π(S^3 - R^3)

And for other problems what does it mean to give the answer in terms of d,R,S

That's correct.

What it means is that your answer must contain only those parameters (your answer cannot contain Q).

 

[twinpair]

And for the other problems, you must give the answer in terms of d,R,S

what does it mean to give the answer in terms of d,R,S?

 

[collinsmark]

Hello twinpair,

Welcome to Physics Forums!

Homework Statement

A thick spherical shell with inner radius R and outer radius S has a uniform charge density d.(A) What is the total charge on the shell? Express your answer in terms of R, S, d, and π. (B) Express the electric field as a function of distance from the center of the sphere r, R, S, d, and the permitivity of free space p for each of the following regions: 0<r<R , R<r<S, S<r

Homework Equations

E = kQ/r2

V=(4/3)πr3

The Attempt at a Solution

(For part A)
Since its a thick shell the volume would be V = (4/3)π(S^3 - R^3)

and dV = Qenc => d=Q/V

so

d = 3Q/(4π(S^3 - R^3))

That's not technically wrong, but it doesn't answer the question. You are already given the density, d. The problem statement is asking you to solve for the total charge, Q.

(For part B)
0<r<R
the electric field will be 0 because the electric field can't close on itself

Correct.

R< r< S
E=kQenc/r2 = (4πkρ(r^3 - R^3))/3r^2

That's the first introduction of ρ, the Greek letter "rho." Is that supposed to be d?

You're supposed to answer in terms of r, R, S, d and p.

Whatever the case, rather than fiddle with substitutions, I suggest starting over. Use Gauss' law.

This part of the problem is very straightforward if you start with Gauss' law; that way it doesn't require any fancy-schmancy substitutions.

S<r
E = kQ/r2 because the sphere can be treated as a point charge and the electric field is symmetric on a sphere

That's also correct, but is using the wrong set of variables. You could make the substitution of $k = \frac{1}{4 \pi p}$, but as it turns out, the solution is actually easier to come by if you apply Gauss' law from start to finish, solving for E as the final step*.

*[Edit: although you can leverage the total charge found in part A.]