Charge on a Sphere: Calc Magnitude & Deficit Electrons

In summary, the conversation discusses the calculation of the charge and number of excess or deficit electrons in a given system. The formula q=Ne is used, where q is the charge and N is the number of electrons. The value for q is found to be 4.8*10^-19, which corresponds to 3 deficit electrons. The units for electric field strength are also discussed, with the conclusion that it is equivalent to V/m. The result of exactly 3 electrons indirectly confirms the correctness of the calculated value.
  • #1
quicksilver123
173
0

Homework Statement



see attachment for pic of diagram and question

b) what is the magnitude of the charge
c) what is the number of excess or deficit electrons?

m=(2.6*10^-15)kg
Δv=265.4V
r=0.005m

Homework Equations



q=Ne
where (q=charge), (e=electron), (N=# of excess/deficit electrons)

ε=ΔV/r

FE = qε

The Attempt at a Solution



FE = Fg
qε=mg
q(ΔV/r)=mg
q=mgr/ΔV

q=(2.6*10^-15)(9.8)(0.005)/265.4
q=4.8*10^-19

The thing is, I tried checking this number and I got some weird values:

ε=kq/r^2
ε=0.0001728

FE=qε
FE=8.2944*10^-23

FE=Fg
8.2944*10^-23 = mg
8.2944*10^-23 = 2.548*10^-14

as you can see... not equal at all.
help?








oh, and assuming B) is correct, here's the answer to C):

q=Ne
N=q/e
N=(4.8*10^-19)/(1.6*10^-19)
N=3

3 deficit electrons, since charge = (+)
 

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  • #2
I don't see any attachment.

ε=kq/r^2
That is related to the electric field from the charged object itself, not the electric field from your setup. If you would work with units, you would see that it does not have the correct units.
 
  • #3
Ah.
What are the units on each and can you tell me of a way to check my answer? I don't see any other method (using different equations) using the set of equations I have.
 
Last edited:
  • #4
There is no alternative way to check your answer, just the formula you used to calculate the value.
Well, the nice result of "exactly" 3 electrons is an indirect way to check the result - a value of 2.5 would be weird.

What are the units on each
I think you should know/determine this yourself.
 
  • #5
ε=kq/r^2
well, i know this one is NC

the other... uhh.. I'm guessing is V/m
which I've never seen before (wasn't used in the course)
 
  • #6
V/m is the electric field strength.
If you mean N/C: Ok, then the units do not show the problem, as N/C = NV/J = V/m
 

Related to Charge on a Sphere: Calc Magnitude & Deficit Electrons

1. What is the charge on a sphere?

The charge on a sphere is the total electric charge present on the surface of a spherical object. It is measured in Coulombs (C).

2. How is the magnitude of charge on a sphere calculated?

The magnitude of charge on a sphere can be calculated using the formula Q = 4πε0r2V, where Q is the charge, ε0 is the permittivity of free space, r is the radius of the sphere, and V is the potential difference between the surface of the sphere and infinity.

3. What is the deficit of electrons on a charged sphere?

The deficit of electrons on a charged sphere refers to the number of electrons that have been transferred or removed from the sphere's surface, resulting in a net positive charge. This deficit can be calculated by dividing the total charge on the sphere by the elementary charge (e = 1.602 x 10-19 C).

4. Can a sphere have a negative charge?

Yes, a sphere can have a negative charge if it has an excess of electrons on its surface, resulting in a net negative charge. The magnitude of the charge can be calculated using the same formula as a positively charged sphere.

5. How does the charge on a sphere affect its electric field?

The charge on a sphere creates an electric field around it, which is strongest at the surface of the sphere. The direction of the electric field lines is determined by the sign of the charge, with positive charges having outward-pointing lines and negative charges having inward-pointing lines. The strength of the electric field is directly proportional to the magnitude of the charge on the sphere.

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