Finding net charge on a sphere's surface

In summary, the conversation discusses the formula for the electric field caused by a surface distribution on a point at a distance of ##a## meters, which is given by $$E(a)=\frac{kQ}{(R+a)^2}$$. The conversation also mentions a calculated value for ##Q##, which is approximately equal to ##4.79\times10^{-8}##, but is missing a minus sign and unit. The conversation ends with a suggestion that the calculation may be incorrect due to a potential bug or incorrect answer in the homework platform.
  • #1
archaic
688
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Homework Statement
We have a thin spherical shell with a spherically symmetric negative charge distribution inside. The radius of the shell is ##R=0.705\,m##, and the electric field strength at its surface is ##E=867\,N/C## everywhere, and is pointing radially toward the center of the sphere.
What is the net charge within the sphere's surface?
Relevant Equations
.
The electric field caused by the surface distribution on a point ##a## meters far from it is$$E(a)=\frac{kQ}{(R+a)^2}$$from which I get$$Q=\frac{(R+a)^2E(a)}{k}=\frac{(R)^2E(0)}{k}=\frac{(0.705)^2\times867}{8.99\times10^9}\approx4.79\times10^{-8}$$and I take its negative because the direction of the field is inwards.
I'm being told that this is wrong, though. Have I misunderstood the question, or approached it incorrectly?
 
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  • #2
Hi. Your answer is numerically correct. (I would use a simple '=' sign though.) Your answer is missing the minus sign and unit.

You should use E(0) = -867N/C (radial sign convention), then you get the missing minus sign in the answer. And never forget units!
 
  • #3
Steve4Physics said:
Hi. Your answer is numerically correct. (I would use a simple '=' sign though.) Your answer is missing the minus sign and unit.

You should use E(0) = -867N/C (radial sign convention), then you get the missing minus sign in the answer. And never forget units!
Thank you! Yes, I know about the negative sign. ;)
archaic said:
and I take its negative
Are you sure, though? This answer is being rejected in my HW platform.
 
  • #4
Hi. Sounds like the HW platform may have a bug or incorrect answer (it happens). Have you tried entering the (incorrect) value without a minus sign? Have you checked any other instructions - e.g. maybe you are meant to enter the answer in nC. Sorry, can't think of anything else.
 
  • #5
Steve4Physics said:
maybe you are meant to enter the answer in nC
Yes... :DD:DD:DD
 
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Related to Finding net charge on a sphere's surface

1. How do you calculate the net charge on a sphere's surface?

The net charge on a sphere's surface can be calculated by using the formula Q = 4πε0r2Φ, where Q is the net charge, ε0 is the permittivity of free space, r is the radius of the sphere, and Φ is the electric flux through the surface of the sphere.

2. What is the significance of finding the net charge on a sphere's surface?

Finding the net charge on a sphere's surface is important in understanding the behavior of electric fields and the distribution of charge on a surface. It can also help in predicting how the sphere will interact with other charged objects.

3. Can the net charge on a sphere's surface be negative?

Yes, the net charge on a sphere's surface can be negative. This indicates an excess of negative charge on the surface of the sphere.

4. How does the net charge on a sphere's surface affect the electric field around it?

The net charge on a sphere's surface affects the electric field around it by creating a radial electric field that points away from the positively charged side and towards the negatively charged side of the sphere. The strength of the electric field is directly proportional to the net charge on the surface.

5. What factors can affect the net charge on a sphere's surface?

The net charge on a sphere's surface can be affected by factors such as the amount and distribution of charge on the sphere, the distance between the sphere and other charged objects, and the presence of any insulating materials that may alter the electric field.

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