Finding the force of repulsion between two point charges

[RabbitWho]

Hello! So this is going into physics because it is a physics problem, but it is maths that is the real problem. So if you came here to help someone with physics and not maths I'm sorry.

1. Homework Statement

Find the force of repulsion between two point charges of +1C and +3C if they are placed 1 m apart in a vacuum. On which charge is the greater force?

So here is what I know

ε=8.9x10^-12
π = 3.14
d = 100 cm
q1 = 1
q2 = 3
cats are soft and warm

Homework Equations

here is the formula I have to use

F= 1/4πε₀ Q₁ Q₂/d²

I can't find pi on the thing. Is this supposed to be pi: π?It looks like a Russian L. This is hard enough without alternate fonts.

The Attempt at a Solution

This is going to be my fourth time trying this.

The correct answer should be 2.682 x 10¹⁰

Am I right in thinking that 10^-2 x 10^-2 =10^-4? It's just 100 x 100 = 10,000, right?

1 (1 x 10 ^-6) ( 3x 10^-6)
_______________________________________________
4π(8.9 x 10^-12)(100)

Here's my attempt at solving what's above the line:

3 x 10 ^-12
________________________________
4π(8.9 x 10^-12)(100)

I'm less confident about what's below. Do I multiply pi by 4 first?

3 x 10 ^-12
________________________________
12.5(8.9 x 10^-12)(100)

Like that?

Am I right in thinking that 8.9 x 10^-12 x 100 = 8.9 x 10^-14?

So now I have

3 x 10 ^-12
______________________________
12.5 (8.9 x 10^-14) 3 x 10 ^-12
____________________________
106.8 x 10^-14)

So there are 2 zeros there that I've put in bold that I think I have to get rid of, and I'm going to add them onto that little -14
1.068 x 10^-16. Is that right? 3 x 10 ^-12
___________________________
1.068 x 10^-16

Now there are loads of zeros above and below the line, am I right in thinking I can cross them out? the difference between -12 and -16 is 4, so I'll get rid of the -12 all together and leave -4 below.

3 x 10
_________________________
1.068 x 10^-4

It occurs to me that 3 x 10 is 30 and that 1.068 x 10000 is 10680

30
______
10680

= 0.00289575289 N

Low and behold.. not the right answer. It is the second time I got this same answer though so at least that's something, I suppose.

I'd really appreciate it if, even something that would inevitably cause me to get the wrong answer happened very early on, you'd tell me if there were other silly things I did with the numbers later.

Thank you!

 

[Buzz Bloom]

Hi Rabbit:

I think your problem may be with units. I suggest you rewrite each of your numeric equations and variable definitions, and include the corresponding units.

Hope this helps.

Regards,
Buzz

 

[TSny]

Am I right in thinking that 10^-2 x 10^-2 =10^-4?

Yes.

It's just 100 x 100 = 10,000, right?

$10^{-2}= \frac{1}{100}$. So, $10^{-2} \times 10^{-2} = \frac{1}{100} \times \frac{1}{100} = \frac{1}{100 \times 100} = \frac{1}{10000} = 10^{-4}$

1 (1 x 10 ^-6) ( 3x 10^-6)
_______________________________________________
4π(8.9 x 10^-12)(100)

The statement of the problem gives the charges as 1 C and 3 C, not 1 x 10^-6 C and 3 x 10^-6 C.

Also, if you are using Coulombs for the charge, then you are working in the SI system of units. In this system of units, the unit of length is the meter, not the centimeter. So, you will need to convert 100 cm to meters.

Here's my attempt at solving what's above the line:

3 x 10 ^-12
________________________________
4π(8.9 x 10^-12)(100)

I'm less confident about what's below. Do I multiply pi by 4 first?

3 x 10 ^-12
________________________________
12.5(8.9 x 10^-12)(100)

Like that?

When you multiply several numbers together, it does not matter what order you multiply them. So, yes, you can multiply π by 4 first.

Am I right in thinking that 8.9 x 10^-12 x 100 = 8.9 x 10^-14?

No. Note that 100 = 10².
So, 10^-12 x 100 = 10^-12 x 10² = 10^-12+2 = 10^-10.

3 x 10 ^-12
____________________________
106.8 x 10^-14)

So there are 2 zeros there that I've put in bold that I think I have to get rid of, and I'm going to add them onto that little -14
1.068 x 10^-16. Is that right?

You are right that you want to add 2 to -14. But that doesn't give you -16.

3 x 10 ^-12
___________________________
1.068 x 10^-16

Now there are loads of zeros above and below the line, am I right in thinking I can cross them out? the difference between -12 and -16 is 4, so I'll get rid of the -12 all together and leave -4 below.

3 x 10
_________________________
1.068 x 10^-4

When you combine the -12 and -16 to get 4, you have used up all the factors of 10 in the numerator. So, your numerator becomes 3, not 3 x 10.

 

[RabbitWho]

Yes.

$10^{-2}= \frac{1}{100}$. So, $10^{-2} \times 10^{-2} = \frac{1}{100} \times \frac{1}{100} = \frac{1}{100 \times 100} = \frac{1}{10000} = 10^{-4}$

cool

The statement of the problem gives the charges as 1 C and 3 C, not 1 x 10^-6 C and 3 x 10^-6 C.

Ah! Sorry, this was a big mistake. I was looking at the sample method, where they were using microunits

Also, if you are using Coulombs for the charge, then you are working in the SI system of units. In this system of units, the unit of length is the meter, not the centimeter. So, you will need to convert 100 cm to meters.

This is confusstipating because in the sample the book has an example with 50 cm and uses 50 as d in the sample method, not 0.5.. But ok!

When you multiply several numbers together, it does not matter what order you multiply them. So, yes, you can multiply π by 4 first.

cool :)

No. Note that 100 = 10².
So, 10^-12 x 100 = 10^-12 x 10² = 10^-12+2 = 10^-10.

Ah yes thank you. Was confusing ^-12 with ¹²

You are right that you want to add 2 to -14. But that doesn't give you -16.

doi *smacks head*

When you combine the -12 and -16 to get 4, you have used up all the factors of 10 in the numerator. So, your numerator becomes 3, not 3 x 10.

Thank you! :) Thank you so much!

 

[RabbitWho]

Homework Statement

[/B]
Find the force of repulsion between two point charges of +1C and +3C if they are placed 1 m apart in a vacuum. On which charge is the greater force?

ε=8.9x10^-12
π = 3.14
d = 100 cm
q1 = 1
q2 = 3

Homework Equations

F= 1/4πε₀ Q₁ Q₂/d²

The Attempt at a Solution

The correct answer should be 2.682 x 10¹⁰

10^-2 x 10^-2 =10^-4

1 x 3
_______________________________________________
4π(8.9 x 10^-12)(1)3
_____________________________
4π(8.9 x 10^-12)(1)

3
_____________________________
12.5(8.9 x 10^-12)(1)

3
___________________________
111.25 x 10 ^-12)

3
___________________
1.125 x 10 ^-10)

=2.67 ^-10N ... X

What am I doing wrong?

So sorry, I did try twice before submitting, and I went over everything for a good 20 minutes.

 

[TSny]

Everything is ok except for the very last step. You did not correctly treat the 10^-10 in the denominator in arriving at your final answer.

What is $\frac{1}{10^{-10}}$?