# Homework Help: Electric Fields and point charges

1. Feb 18, 2012

### beachy6

1. The problem statement, all variables and given/known data

A point charge −3 pC is concentric with two
spherical conducting thick shells, as show in
the ﬁgure below. The smaller spherical conducting shell has a net charge of 22 pC and
the larger spherical conducting shell has a net
charge of 18 pC.

1-4)Answer in units of pC
What is the charge on the inner surface of
the smaller spherical conducting shell, 1.2 cm
from the −3 pC point charge? Under static
conditions, the charge on a conductor resides
on the surface of the conductor.
Answer in units of pC

What is the charge on the outer surface of
the smaller spherical conducting shell, 4.1 cm
from the −3 pC point charge?

What is the charge on the inner surface of the
larger spherical conducting shell, 6 cm from
the −3 pC point charge?

What is the charge on the outer surface of the
larger spherical conducting shell, 8.8 cm from
the −3 pC point charge?

5-9)Answer in units of N/C
What is the magnitude of the electric ﬁeld at
P1, 0.6 cm from the −3 pC point charge?

What is the magnitude of the electric ﬁeld at
P2, 2.65 cm from the −3 pC point charge?

What is the magnitude of the electric ﬁeld at
P3, 5.05 cm from the −3 pC point charge?

What is the magnitude of the electric ﬁeld at
P4, 7.4 cm from the −3 pC point charge?

What is the magnitude of the electric ﬁeld at
P5, 10.2 cm from the −3 pC point charge?

2. Relevant equations
electric flux= in E*dA
E=(kq/r^2)

3. The attempt at a solution
I started solving these and I know I have to use Gauss Law, I know I need to apply Gauss law for different radii but when i try set it up electric flux= in E*dA I dont seem to get it. I have tried several different ways

I know that 6 and 8 are 0 because they are in the conductor.
7 i used E=(kq/r^2)

but i have been really confused on the rest of them.

I have tried many different equations but have been confused on different lengths! If someone could at least lead me in the right direction I would really appreciate it!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 18, 2012

### ehild

Make a drawing. What is the electric field inside the shells? Show the surface charge densities on the shells, and show your work in detail, please.

ehild

3. Feb 18, 2012

### beachy6

Here is a picture. I drew it myself so it may not be the best drawn picture, but it is accurate to the problem. Thanks a lot for the help!

#### Attached Files:

• ###### physics pic.jpg
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4. Feb 18, 2012

### ehild

Nice picture!

You know that the charges of a metal accumulate on the surface, and the electric field is zero inside the metal.
Also the number of electric field lines crossing a unit surface normally is equal to the surface charge density divided by ε0.

So what is the charge on the inner surface of the smaller shell?

ehild

5. Feb 18, 2012

### beachy6

Wouldnt the charge of the inner surface of the smaller shell simply E*dA, since the radius is 1.2 cm (0.012m) would it be

E*dA= (-3pC)*(pi*0.012^2)?

6. Feb 18, 2012

### ehild

εI do not understand what you wrote. The whole charge on the inner surface is εEA.
What is the electric field at 0.012 m from the centre?

ehild

7. Feb 18, 2012

### beachy6

Would you do take the area and multiply it by the charge? so (pi)(r^2)(-3pC)?

8. Feb 18, 2012

### mmiller12

hmmmm i tried using E=q/SA, which was not correct either.
Not exactly sure where to go from here then

sorry bud

Last edited: Feb 19, 2012
9. Feb 18, 2012

### ehild

The electric field has to be multiplied by ε0 and the surface area of the sphere. -3 pC is a point charge. What is the electric field at a distance r=0.012 m from it, according to Coulomb's law?

ehild

Last edited: Feb 19, 2012
10. Feb 18, 2012

### beachy6

Electric field would be equal to the point charge/ (surface area)(ε0) correct?

11. Feb 18, 2012

### beachy6

So for number one when it asks "What is the charge on the inner surface of
the smaller spherical conducting shell, 1.2 cm
from the −3 pC point charge? would i use the equation
q=(electric field)(surface area)(E0)

but how do i fiend the electric field?

12. Feb 18, 2012

### beachy6

This problem is so frustrating! I have tried everything possible i feel like. Anyone know if for numbers 7 and 9 we have to take into account the conuctors and subtract the radius by the width of the conductor?

13. Feb 18, 2012

### ehild

Answer question 1 first. Show what you tried.

ehild

14. Feb 19, 2012

### ehild

Look at your previous post.
Take the direction of the electric field into account. What kind of charge does accumulate on the inner surface, positive or negative?
ehild

15. Feb 19, 2012

### beachy6

Since it is in the inner surface it would be a negative because the formula is -q/4pir^2

Once i find the electric field, how do i use this to find the charge? we have tried E*Area=Q/E0

16. Feb 19, 2012

### mmiller12

This is a really tough problem. You might need to take a question like this to a professor or someone at your school. I usually try to get help from a professor during office hours. A problem like this might be too difficult for you to get help from people on physics forum. It is very involved. Hope you have good luck on this site though,

17. Feb 19, 2012

### ehild

We try on the other way. There is a negative point charge in the middle. The electrons of the metal shell are free to move. Are they attracted or repulsed by the -3 pC charge?

ehild

18. Feb 19, 2012

### beachy6

Ya i have asked several of my friends who have taken this class for help but they all could not remember exactly how to do a problem like this. My professor has really bad office hours and is not too helpful... thanks tho for the advice

19. Feb 19, 2012

### beachy6

repulsed

20. Feb 19, 2012

### ehild

OK. So what kind of charges remain on the inner surface if the negative charges are repulsed away?

ehild