Two concentric conducting spherical shells, find outer Q

[mattz205]

Homework Statement

Two concentric conducting spherical shells produce a radially outward electric field of magnitude 49,000 N/C at a point 4.10 m from the center of the shells. The outer surface of the larger shell has a radius of 3.75 m. If the inner shell contains an excess charge of -5.30 μC, find the amount of charge on the outer surface of the larger shell. (k

Homework Equations

closed surface int(E dot dA) = Q encl/epsilon0 (gauss's law)

The Attempt at a Solution

I plugged in the given electric field into gauss's law in the form E=Q encl/ 4pir^2 epsilon0, with Q encl= q(inner)+ q(outer) and solved for q(outer) and arrived at ~ 96.9 μC but that is wrong according to MP (my homework site)

any help would be greatly appreciated

 

[SammyS]

Homework Statement

Two concentric conducting spherical shells produce a radially outward electric field of magnitude 49,000 N/C at a point 4.10 m from the center of the shells. The outer surface of the larger shell has a radius of 3.75 m. If the inner shell contains an excess charge of -5.30 μC, find the amount of charge on the outer surface of the larger shell. (k

Homework Equations

closed surface int(E dot dA) = Q encl/epsilon0 (gauss's law)

The Attempt at a Solution

I plugged in the given magnetic field into gauss's law in the form E=Q encl/ 4pir^2 epsilon0, with Q encl= q(inner)+ q(outer) and solved for q(outer) and arrived at ~ 96.9 μC but that is wrong according to MP (my homework site)

any help would be greatly appreciated

First of all it's not a magnetic field (I suppose that was a typo).

How much charge is there on the inner surface of the outer larger shell?

 

[mattz205]

First of all it's not a magnetic field (I suppose that was a typo).

How much charge is there on the inner surface of the outer larger shell?

Yes, sorry about that i meant electric field, and wouldn't the charge on the inner surface of the outer shell just be the negative of the outer? If that's not it then I'm not entirely sure.

 

[Qwertywerty]

Yes, sorry about that i meant electric field, and wouldn't the charge on the inner surface of the outer shell just be the negative of the outer? If that's not it then I'm not entirely sure.

No , not necessarily . This would be true if the outer shell itself had no excess charge .

I couldn't understand your solution - have you equated electric field to kq/r² (where q is charge on the outer surface of the outer sphere ) ?

 

[SammyS]

Yes, sorry about that i meant electric field, and wouldn't the charge on the inner surface of the outer shell just be the negative of the outer? If that's not it then I'm not entirely sure.

The charge on the inner surface of the outer shell would just be the negative of the outer shell only if the outer shell has a net charge of zero. That's not stated anywhere. Besides if that was true, then the total charge inside the Gaussian surface (the closed surface you mention) would have to be -5.30 μC .

Consider a Gaussian surface totally embedded in the conducting material of the large sphere. What's the total charge enclosed by this surface ?

 

[mattz205]

The charge on the inner surface of the outer shell would just be the negative of the outer shell only if the outer shell has a net charge of zero. That's not stated anywhere. Besides if that was true, then the total charge inside the Gaussian surface (the closed surface you mention) would have to be -5.30 μC .

Consider a Gaussian surface totally embedded in the conducting material of the large sphere. What's the total charge enclosed by this surface ?

the electric field inside a conductor is always zero according to my lecture... and the charge enclosed there would be the -5.3 + whatever the inner surface of the conductor is, which i don't know, nor do i know how to find it...

 

[SammyS]

the electric field inside a conductor is always zero according to my lecture... and the charge enclosed there would be the -5.3 + whatever the inner surface of the conductor is, which i don't know, nor do i know how to find it...

If the electric field is zero, then the flux through that Gaussian surface is zero. That tells you total charge enclosed is ___ .

 

[mattz205]

If the electric field is zero, then the flux through that Gaussian surface is zero. That tells you total charge enclosed is ___ .

0? would that make the charge on the inside of the conductor +5.3?

 

[Pyrus]

I tried this by using E=V/r. I found potential at point at distance 4.1 m.
V=Er => V=20900 V
Then applying V= 1/(4πε) * {q/4.1 + Q/4.1}
V=(9*10^9 )[-5.3/4.1 + Q/4.1]*10^-6

Solving it I also got answer 96.6μC

 

[mattz205]

I tried this by using E=V/r. I found potential at point at distance 4.1 m.
V=Er => V=20900 V
Then applying V= 1/(4πε) * {q/4.1 + Q/4.1}
V=(9*10^9 )[-5.3/4.1 + Q/4.1]*10^-6

Solving it I also got answer 96.6μC

i tried that method too and got the same answer as i did using the other method, the answer is wrong regardless though

 

[mattz205]

If the electric field is zero, then the flux through that Gaussian surface is zero. That tells you total charge enclosed is ___ .

ok, ok, i got it, thank you very much for your help!

 

[Pyrus]

So simple and I got it too complex...

 

[SammyS]

0? would that make the charge on the inside of the conductor +5.3?

Yes.

ok, ok, i got it, thank you very much for your help!

Notice that your final answer is independent of the amount of charge on the inner sphere. The conductor effectively shields the region outside of the sphere from the region inside the sphere.

 

[mattz205]

Notice that your final answer is independent of the amount of charge on the inner sphere. The conductor effectively shields the region outside of the sphere from the region inside the sphere.

That makes sense, in lecture my instructor wasn't very clear about how conductors worked, but it makes sense now. Thnk you again for your help, i greatly appreciate it.