Electromagnatism - Find charge deos this sphere have

In summary, the problem involves finding the charge of a small conducting ball suspended by the force of gravity and the force between it and a sphere with a fixed positive charge. After rearranging the equations and using the value of (1/(4 x pi x epsilon 0)) = 9x10^9, the charge of the ball is calculated to be 4.9 x 10^-9 C.
  • #1
uniidiot
24
0

Homework Statement


The centre of a small sphere carrying a positive charge of 1.0 x 10^-8 C is fixed at 3cm above the centre of a small conducting ball, which had a negative charge and a mass of 0.05g. If the ball remains suspended, what charge does it have?

Answer is [ 4.9 x 10^-9]

but i can't seem to get that answer


Homework Equations





The Attempt at a Solution



Because the ball is suspended i take it that the force between the two charged bodies must be equal but opposite to the force due to gravity so:

F = mg

F = 0.05 x 9.8 = 0.49

F = (1/(4 x pi x epsilon 0)) x ((Q1 Q2) / r^2)

(1/(4 x pi x epsilon 0)) = 9 x 10^9

F = 9 x 10^9 x (Q1 Q2 / r^2)

Q2 = 9 x 10^9 x (Q1 / (r^2 x F)

Q2 = 9 x 10^9 x (10^-8 / (3^2 x 0.49)

Q2 = 20.4



please help :confused::confused::confused:
 
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  • #2
uniidiot said:
F = mg

F = 0.05 x 9.8 = 0.49
Check your units.

F = (1/(4 x pi x epsilon 0)) x ((Q1 Q2) / r^2)

(1/(4 x pi x epsilon 0)) = 9 x 10^9

F = 9 x 10^9 x (Q1 Q2 / r^2)
OK.

Q2 = 9 x 10^9 x (Q1 / (r^2 x F)
Not sure what you did here.

Solve the problem algebraically first. Set your two equations for F equal to each other and solve for Q. The last step is to plug in numbers.
 
  • #3
Quote:
Originally Posted by uniidiot View Post
F = mg

F = 0.05 x 9.8 = 0.49
Check your units.

i see what I've done, it should be in Kg not g

so

F = 0.00005 x 9.8 = 4.91 x 10^-4


Quote:
F = (1/(4 x pi x epsilon 0)) x ((Q1 Q2) / r^2)

(1/) = 9 x 10^9

F = 9 x 10^9 x (Q1 Q2 / r^2)
OK.

Quote:
Q2 = 9 x 10^9 x (Q1 / (r^2 x F)
Not sure what you did here.

Solve the problem algebraically first. Set your two equations for F equal to each other and solve for Q. The last step is to plug in numbers.

ok well:

F = x ((Q1 Q2) / r^2)

so if i rearrange to get Q2

Q2 = (1/(4 x pi x epsilon 0)) x (Q1 / (r^2 x F)

yes?
 
  • #4
uniidiot said:
F = x ((Q1 Q2) / r^2)

so if i rearrange to get Q2

Q2 = (1/(4 x pi x epsilon 0)) x (Q1 / (r^2 x F)

yes?
No. Redo that algebra. How did you get Q2 on the left side? (Looks like you divided by Q2 on the right, but multiplied by Q2 on the left. You have to do the same operation to both sides of an equation.)
 
  • #5
ah, stupid me!

so

Q2 = (1/(4 x pi x epsilon 0)) x ((Q1 x f) / r^2)

Q2 = (9 x 10^-9) x (((1.0 x 10^-8) x (4.9 x 10^-4)) / 3^2)

Q2 = 4.9 x 10^-3

i, getting closer but, the answer should be 4.9 x 10^-9

i thought it might be the units but they seem ok now
 
  • #6
algebra error

uniidiot said:
so

Q2 = (1/(4 x pi x epsilon 0)) x ((Q1 x f) / r^2)
This is not true. You are taking an equation like this:
F = A*B

And transforming it into this:
A = B/F (NO GOOD!)

(Imagine A & B are your Q1 & Q2)

But you should get:
1/A = B/F

Which can be inverted to be:
A = F/B

Try this. Redo your algebra as I suggested earlier.
 
  • #7
ok, ignoring (1/(4 x pi x epsilon 0)) for the minute

F = ( Q1 Q2 )/ r^2

F / Q2 = Q1 / r^2

1 / Q2 = Q1 / (F x r^2)

Q2 = (F x r^2) / Q1
 
  • #8
You are back on track now.
 
  • #9
just plug in the values with appropriate units now
 
  • #10
Thanks for everyones help =)

but i still can't get the corect answer:

Q2 = ((F x r^2) / Q1) x (1/(4 x pi x epsilon 0))

Q2 = ((4.91x10^-4 x 3^2) / 10^-8) x (9x10^9) = 3.97x10^15

Above the question it is stated that
(1/(4 x pi x epsilon 0)) = 9x10^9

i still can't see how I am not getting [ 4.9 x 10^-9 C ]
 
  • #11
uniidiot said:
Thanks for everyones help =)

but i still can't get the corect answer:

Q2 = ((F x r^2) / Q1) x (1/(4 x pi x epsilon 0))
Your "(1/(4 x pi x epsilon 0))" is in the wrong place. It should be right next to Q1.

If you let k = (1/(4 x pi x epsilon 0)), then you have:
mg = k Q1 Q2/r^2

Solve for Q2 again (so you see where the k goes) and then plug in the numbers.
 
  • #12
try to do it on paper if you are not already
because writing things out clearly with appropriate symbols is much simpler
than saying (1/4 x pi x epsilon)) x (((F x r^2) / Q1))...and so on
 

1. What is electromagnetism?

Electromagnetism is a branch of physics that deals with the study of electromagnetic forces, which are the forces responsible for the interactions between electrically charged particles.

2. How is electromagnetism related to charge?

Electromagnetism is closely related to charge because charges create electric fields and moving charges create magnetic fields. The interaction between these fields is what gives rise to electromagnetic forces.

3. How do you find the charge of an object?

The charge of an object can be found by using Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

4. What is the unit of charge?

The unit of charge is the Coulomb (C), named after French physicist Charles-Augustin de Coulomb. It is defined as the amount of charge that passes through a point in an electric circuit in one second when the current is one ampere.

5. How can you determine the charge of a sphere?

To determine the charge of a sphere, you can use the formula Q = 4πεr²E, where Q is the charge, ε is the permittivity of the material, r is the radius of the sphere, and E is the electric field at the surface of the sphere. This formula assumes that the sphere is a perfect conductor and has a uniform charge distribution.

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