Surface charge density of spherical conductor with given potential

[NINHARDCOREFAN]

Stuck on surface charge density problem.

Calculate the surface charge density for a solid spherical conductor of radius .438m if the potential is .876m from the center of the sphere is 1.87kV. Answer in units of C/m^2

Ok I did this:
V= Kq/r
q= V*r/k
q= 1.87e-3*.876/8.99e9
q= 1.822e-13

E= kq/r^2
E= 8.99e9*1.88e-13/.438^2
E= 8.809e-3

SCD= 2*epsilon*E
SCD= 1.559e-13

But it's wrong.

The only thing I'm not sure about is the Electric field.

 

[paul11273]

I am learning this material right now, but here goes a stab:

I think you calculated the total charge of the sphere correctly.
Assuming that q=1.822*10^-13, I think the next step is to simply divide this by the area of the sphere:
SCD=Q/A
SCD=1.822*10^-13 (C)/ 4*pi*r^2
SCD=1.822*10^-13 (C)/ 4*pi*(.438m)^2
SCD=1.822*10^-13 (C)/ 4*pi*(.191844m^2)
SCD=7.55*10^-14 (C/m^2)

I hope that is the answer. If not, I would really like someone else to let us know where our errors are. I am learning this material too, but figured I would give it a try.

Thanks.

 

[Norman]

Your radial distance in your potential equation is incorrect. Also, why are you trying to find the E-field at the surface of the sphere? That is going to be ill-defined. Listen to paul he has the correct method. Also 1.87 kV = 1.87e+3 V not to e-3.
Good luck.

 

[NINHARDCOREFAN]

...

I am learning this material right now, but here goes a stab:

I think you calculated the total charge of the sphere correctly.
Assuming that q=1.822*10^-13, I think the next step is to simply divide this by the area of the sphere:
SCD=Q/A
SCD=1.822*10^-13 (C)/ 4*pi*r^2
SCD=1.822*10^-13 (C)/ 4*pi*(.438m)^2
SCD=1.822*10^-13 (C)/ 4*pi*(.191844m^2)
SCD=7.55*10^-14 (C/m^2)

I hope that is the answer. If not, I would really like someone else to let us know where our errors are. I am learning this material too, but figured I would give it a try.

Thanks.

Forgot to tell that I also tried that. Thanks for trying though.

Your radial distance in your potential equation is incorrect. Also, why are you trying to find the E-field at the surface of the sphere? That is going to be ill-defined. Listen to paul he has the correct method. Also 1.87 kV = 1.87e+3 V not to e-3.
Good luck

When using V in calculations, it should be in V not KV so that's why it's 1.87e-3

 

[paul11273]

At the risk of sounding dumb, what should his radius be in the potential equation?

 

[NINHARDCOREFAN]

At the risk of sounding dumb, what should his radius be in the potential equation?

radius .438m if the potential is .876m

.876m because it's telling the potential from that distance. You did the same calculations as I did.

 

[paul11273]

Since you seem to know E JUST outside the conductor, I found in my text where:

E=SCD/epsilon

So can we use this rearranged to solve for SCD?

 

[NINHARDCOREFAN]

I did that, it's in the first post but it's wrong I don't know why

SCD= 2*epsilon*E
SCD= 1.559e-13

 

[paul11273]

Right, I should have realized before I posted that is where the 2*epsilon*E came from. I guess I thought I was onto something and got excited. Should have ran the numbers first.

Does you book have an answer for this problem? Maybe we can back into it?

 

[NINHARDCOREFAN]

This is an online howework question. Answers aren't posted until after the due date.

 

[paul11273]

2*epsilon*E

Where does the 2 come from?

 

[paul11273]

I am calling it a night. I will pick up with this one in the morning. Hopefully I will be a little sharper.

 

[NINHARDCOREFAN]

Never mind my friend did it for me, he got 7.558366e-8 and it's right

 

[paul11273]

Can you let me know how he got that? I am curious now.

 

[NINHARDCOREFAN]

Q = ( bigR * V ) / K

then Q / a
a = 4pi small r ^2

V= 1870

that's where we went wrong