Calculate the number of excess electrons

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In summary, two negatively charged objects with a force of 6.3 N and distance of 0.5 cm are used to calculate the number of excess electrons on the second object, given that one object has 8.3 x 10^22 extra electrons. Using Coulomb's Law and the equation q1 = F*r^2/(k*q2), it is determined that the second object has 1.3 x 10^-18 C of excess charge, which is equivalent to 8.1e electrons.
  • #1

Homework Statement



Two negatively charged objects repel each other with a measured force of 6.3 N when they are 0.5 cm apart. If the excess charge on one of the objects is caused by 8.3 x 10^22 extra electrons, use Coulomb's Law to calculate the number of excess electrons on the second object.



Homework Equations



F=kq1q2/r^2



The Attempt at a Solution



Since 1e=1.602 x 10^-19C
8.3 X 10^22e = (1.602 x 10^-19 C)(8.3 x 10^22)
=1.3 x 10^4 C

Therefore, 6.3N = (9 x 10^9 N*m^2/C^2)1.3 x 10^4 C)(q2)/(0.005m)^2
=1.3 x 10^-18 C

Since 1C = 6.242 x 10^18e
1.3 x 10^-18C = (1.3 x 10^-18)(6.242 x 10^18)e
=8.1e ?


I think I might be over complicating this one. Can anybody help me out? Please?
 
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  • #2
Hi, i don't understand what you've done.

6.3N = (9 x 10^9 N*m^2/C^2)1.3 x 10^4 C)(q2)/(0.005m)^2
=1.3 x 10^-18 C

What is this ? 6.3N=1.3x10^-8 C ?

If you write a=b then a should equal b. You are confused.
Here's a tip - don't put in the numbers until you have worked out an algebraic formula for what you want. You want q1, and then to divide by the electronic charge.
 
  • #3
would this equation be all right?

q1=F(r)^2/k(q2)
 
  • #4
Yes, good, but better written like this ( because F(r) looks like a function)

q1 = F*r^2/(k*q2)

It's also clearer if you show the multiplication sign. Now plug in the numbers and then divide by the electronic charge.
 
  • #5
:smile: Thanks Mentz! I was over complicating it. Smooth sailing now though!
 

1. What is the formula for calculating the number of excess electrons?

The formula for calculating the number of excess electrons is n = Q/e, where n is the number of excess electrons, Q is the excess charge, and e is the elementary charge (1.602 x 10^-19 Coulombs).

2. How do you determine the excess charge in a system?

The excess charge can be determined by subtracting the total number of protons in the system from the total number of electrons. A positive result indicates an excess of electrons, while a negative result indicates a deficiency of electrons.

3. Can the number of excess electrons be a decimal or fraction?

No, the number of excess electrons must be a whole number as it represents the actual number of electrons in a system. If the result of the calculation is a decimal or fraction, it should be rounded to the nearest whole number.

4. Is the number of excess electrons always constant?

No, the number of excess electrons can change depending on the conditions of the system. For example, if more electrons are added to the system or some electrons are removed, the number of excess electrons will change accordingly.

5. What is the significance of calculating the number of excess electrons?

Calculating the number of excess electrons is important in understanding the behavior and properties of a system. It can also help in studying the effects of excess charge on the system and determining the appropriate measures to balance the charge.

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