Cylindrical Shells and Gauss' Law

[Soaring Crane]

Homework Statement

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density sigma = 12 nC/m^2. The electric field at r = 5.9 cm is approximately


a.0.81 kN/C

b.zero.

c.1.3 kN/C.

d.12 kN/C.

e.0.56 kN/C.

Homework Equations

See below.

The Attempt at a Solution

Will the correct choice be b. 0? I am assuming that this is a conducting cylindrical shell. When r < R, E will be 0.

Homework Statement

An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density rho = 200 nC/m^3. What is the electric field at r = 8.0 cm?


a.0.23 kN/C

b.0.11 kN/C

c.57 kN/C

d.0.44 kN/C

e.zero

Homework Equations

electric flux = Integral [E*dA] = Q_enclosed/epsilon_0

The Attempt at a Solution

I sloshed through this one because I mixed up the radii (r and R) at first. Did I eventually get the correct answer?

Q_enclosed = rho*2*pi*R^2*l

flux = E*2*pi*r*l

E*2*pi*r*l = (rho*2*pi*R^2*l)/(epsilon_0)

E = (rho*R^2)/(r*epsilon_0) = (200*10^-9 c/m^3)(0.04 m)^2/[0.08 m*8.85*10^-12] = 452 N/C??



Thanks.

 

[Doc Al]

Homework Statement

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density sigma = 12 nC/m^2. The electric field at r = 5.9 cm is approximately


a.0.81 kN/C

b.zero.

c.1.3 kN/C.

d.12 kN/C.

e.0.56 kN/C.

Homework Equations

See below.

The Attempt at a Solution

Will the correct choice be b. 0? I am assuming that this is a conducting cylindrical shell. When r < R, E will be 0.

No reason to think the shell has any thickness or that it's a conductor. Nonetheless, since the charge is on the surface of the shell (and we presume no other charge exists) the field will be zero for r < R. (Since the charge enclosed within any cylindrical shell with such a radius would be zero.)

Homework Statement

An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density rho = 200 nC/m^3. What is the electric field at r = 8.0 cm?


a.0.23 kN/C

b.0.11 kN/C

c.57 kN/C

d.0.44 kN/C

e.zero

Homework Equations

electric flux = Integral [E*dA] = Q_enclosed/epsilon_0

The Attempt at a Solution

I sloshed through this one because I mixed up the radii (r and R) at first. Did I eventually get the correct answer?

Q_enclosed = rho*2*pi*R^2*l

flux = E*2*pi*r*l

E*2*pi*r*l = (rho*2*pi*R^2*l)/(epsilon_0)

E = (rho*R^2)/(r*epsilon_0) = (200*10^-9 c/m^3)(0.04 m)^2/[0.08 m*8.85*10^-12] = 452 N/C??

I didn't check your arithmetic, but your method is correct.

 

[m2003]

I would like to confirm that your answers are correct. In the first problem, since the cylindrical shell is conducting, the electric field inside the shell is zero. Therefore, the correct answer is b. zero.

In the second problem, your calculations are correct and the answer is indeed 452 N/C. Good job on catching the mistake with the radii and correcting it. Keep up the good work!