Electrostatics: Creating Charged Objects

[Snape1830]

An iron arrowhead has an initial charge of 2.100e-6 C. How many electrons are required to give it a charge of −2.82 μC?

I know that e (the elementary charge) = +/- 1.602E-19 C
And N is the number (or excess charge)

I tried solving this problem 2 ways. The first way:

(2.100E-6 - 2.82E-6)/1.602E-19
I got 4.45E12 electrons

The second way I did:
2.100E-6-1.602E-19 * N = -2.82E-6
-1.602E-19 * N = -2.82E-6 - 2.100E-6
N =-4.92E6/-1.602E19
N= 3.05E25 electrons

However, my homework says it's wrong I tried typing them in with a negative sign, it's wrong. I tried rounding to the nearest electrons, still wrong.
What am I doing wrong? I really have no idea!

 

[SammyS]

An iron arrowhead has an initial charge of 2.100e-6 C. How many electrons are required to give it a charge of −2.82 μC?

I know that e (the elementary charge) = +/- 1.602E-19 C
And N is the number (or excess charge)

I tried solving this problem 2 ways. The first way:

(2.100E-6 - 2.82E-6)/1.602E-19
I got 4.45E12 electrons

The second way I did:
2.100E-6-1.602E-19 * N = -2.82E-6
-1.602E-19 * N = -2.82E-6 - 2.100E-6
N =-4.92E6/-1.602E19
N= 3.05E25 electrons

However, my homework says it's wrong I tried typing them in with a negative sign, it's wrong. I tried rounding to the nearest electrons, still wrong.
What am I doing wrong? I really have no idea!

The arrowhead initially has a positive charge. The first 2.100×10^-6 C worth of electrons are needed to neutralize the initial positive charge.

 

[Tsunoyukami]

You begin with a charge of 2.1e(-6) C. You need to add electrons until you have a charge of -2.82e(-6) C. This means you need to add enough electrons such that the total charge of all the electrons added is equal to the difference in these charges; that is, the total charge of all the eletrons you add must be [2.1e(-6) - (-2.82e(-6)] C.

 

[Snape1830]

The arrowhead initially has a positive charge. The first 2.100×10^-6 C worth of electrons are needed to neutralize the initial positive charge.

So would I divide 2.100E-6 by -1.602E-19?

 

[Snape1830]

You begin with a charge of 2.1e(-6) C. You need to add electrons until you have a charge of -2.82e(-6) C. This means you need to add enough electrons such that the total charge of all the electrons added is equal to the difference in these charges; that is, the total charge of all the eletrons you add must be [2.1e(-6) - (-2.82e(-6)] C.

So 7.27E-7. What do I do from there?

I only have a couple tries left on my homework and I want to get it right.

 

[Tsunoyukami]

I believe you have found the difference in charge incorrectly; you did 2.1e(-6) - 2.82e(-6) but you need to make it 2.1e(-6) - (-2.82e(-6)) so that it becomes addition and you get:

2.1e(-6) + 2.82e(-6) = 4.92e(-6) C

So the total number of electrons required woul have charge equal to 4.92e(-6). So what would you do next?

[Another way to think about it is that you need x electrons to reduce the charge from 2.1e(-6) to 0 and then another y electrons to reduce the charge from 0 to -2.82e(-6). If you sum x and y together you should find the same number as you will from the method I explained above.]

 

[Snape1830]

I believe you have found the difference in charge incorrectly; you did 2.1e(-6) - 2.82e(-6) but you need to make it 2.1e(-6) - (-2.82e(-6)) so that it becomes addition and you get:

2.1e(-6) + 2.82e(-6) = 4.92e(-6) C

So the total number of electrons required woul have charge equal to 4.92e(-6). So what would you do next?




[Another way to think about it is that you need x electrons to reduce the charge from 2.1e(-6) to 0 and then another y electrons to reduce the charge from 0 to -2.82e(-6). If you sum x and y together you should find the same number as you will from the method I explained above.]

Wouldn't I divide that number by e? Then I get 3.07E13 electrons.

 

[Tsunoyukami]

Yes, that is correct. You can try it the second way I mentioned to convince yourself that they are equivalent.

 

[Snape1830]

Yes, that is correct. You can try it the second way I mentioned to convince yourself that they are equivalent.

I was holding my breath as I typed it into my answer key, waiting for the check! Thanks so much! I really appreciate it!

 

[Tsunoyukami]

I'm glad to have been of assistance. Hopefully you've learned something from this. :)