# Electric field problem

1. Jul 1, 2012

### Saitama

1. The problem statement, all variables and given/known data
Match the entries of Column-I with entries of Column-II

E is the electric field vector.
There can be more than one answer for each entry in column-I.

2. Relevant equations

3. The attempt at a solution
I am not sure about any of the answer and i don't have the answer key too.
I would like to discuss each entry in Column-I one by one.
For the first question, i suppose the answer should be r) and t) because the conductor is neutral and the potential will be due to the point charge and electric field will be produced by the point charge kept near to the conductor. Is my reasoning correct?

EDIT: 800th post. :D

Last edited: Jul 1, 2012
2. Jul 1, 2012

### ehild

Congratulation for the 800th post. But why do you think that the magnitude of E varies in the void inside the conductor if there is no charge there? The charge is outside. What does Gauss' law state?

ehild

3. Jul 1, 2012

### pcm

there will also be the contribution of induced charges on the conductor surface (the net induced charge being zero) on the potential and field inside it.
the field inside a conductor is independent of the charges outside it.if you bring another charge outside ,although the distribution of charge on conductor surface will change but the field inside will remain same.
in fact in this case field is zero.

4. Jul 1, 2012

### Saitama

Thank you ehild, i understand it now. By Gauss law there would be no electric field inside the conductor. But what about the potential? I think it should be constant because inside the conductor, E is zero, therefore -dV/dr=0 or dV=0, therefore V is constant. So the answer should be p) and s) ?

5. Jul 1, 2012

### ehild

If the electric field is zero the potential is constant. Moreover, the potential is a continuous function, it is the same at both sides of the inner surface of the metal shell, inside the void and inside the metal layer. You are right, p) and s) in column II matches to case a) in column I.

ehild

6. Jul 1, 2012

### Saitama

Not sure about q), i guess |E| should also be zero.

7. Jul 1, 2012

### pcm

yes,|E| is also zero.

8. Jul 1, 2012

### Saitama

Thanks!
Can i have some hints for part b)?

9. Jul 1, 2012

### ehild

Gauss? You surround the point charge with a sphere. Can E = 0 everywhere on its surface?

ehild

10. Jul 1, 2012

### Saitama

No, E is not zero on the surface if we surround the point charge with a sphere.

11. Jul 1, 2012

### ehild

Yes. So are p) and q) true if E somewhere inside the shell differs from zero?

ehild

12. Jul 1, 2012

### Saitama

No p) and q) are not true.

r) should be the correct answer. As E is varying, potential should also vary, therefore the answer should be r) and t). Am i right?

13. Jul 1, 2012

### ehild

Yes. they are true, but can you explain why is |E| varying?

ehild

14. Jul 1, 2012

### Saitama

Electric field inside the conductor is due to the point charge and it varies inversely with the square of distance from the charge, therefore the magnitude of E should also vary. Is my explanation correct?

15. Jul 1, 2012

### ehild

Almost.The point charge is not alone, it is surrounded by the metal shell and there is some induced surface charge distribution in the inner surface. The electric field is due to the point charge and that surface charge distribution. In general, the field is not the same as that of a single point charge, but because of spherical symmetry, it is.

There comes the next step, c. What do you think?

ehild

16. Jul 1, 2012

### Saitama

Thanks ehild!

About c, i am confused, it seems like the combination of both parts, a) and b). Applying Gauss law and surrounding the charge q2 with a sphere, E is not zero on the surface of sphere. E is varying inside and hence the potential is also varying. The answer should be again r) and t) but i think i am doing something wrong as their is still a charge q1 present. q1 is scaring me.

17. Jul 1, 2012

### ehild

Do not be scared by q1. It induces a charge distribution on the outer surface of the metal shell, but the field is still zero inside the metal wall. The outer field does not penetrate into the void. The point charge q2 inside does not feel anything, it just does not know about the presence of q1 so it is not scared of it, why are you?

ehild

18. Jul 1, 2012

### Saitama

How the electric field is zero?
In the part b), E was present in conductor when a charge is kept inside but why here it is zero? I don't get the point here. :(

19. Jul 1, 2012

### ehild

The electric field is zero in the metal wall, not in the void it surrounds.

ehild

20. Jul 1, 2012