I'm new here, can someone help me with a problem regarding charge?

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In summary, the conversation revolves around a physics problem regarding charges and net force. The problem involves a charge of -5q placed at x=0 and a charge of +3q placed at x=10. The question is where on the x-axis the net force on a charge Q would be zero. After some discussion and confusion, the answer is determined to be x=44.4, found using the equation F = -5qQ/(4*pi*e0*x^2) + 3qQ/(4*pi*e0*(x-10)^2). The conversation ends with gratitude and a bit of humor.
  • #1
echau
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Hi, I'm new here and I was wondering if anyone can help me with a physics problem regarding charge. Any input would be greatly appreciated!

A charge -5q is placed at x=0 and a charge +3q is placed at x=10. Where on the x-axis is the net force on a charge Q zero?

The answer is x=44.4.

Can anyone hlep me solve this? Thanks!
 
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  • #2
Are you sure that's the right way round? Or that the answer isn't negative? If the greater, positive charge is at x=10, then for any x > 10 there will be a net charge (except at infinity), since the nearest charge is the greatest of the two opposite charges.

Either the two charges need to be swapped around, or the answer is negative, or the answer is between 0 and 10. Double-check.
 
  • #3
Welcome to PF, by the way.
 
  • #4
I typed it exactly as it is in the book. It really has me confused.

The third charge is not given.
So far it is -5q, +3q, and ?q.
The net force on the charge is zero.

Is there any way to figure out the third charge so that the net force would be zero?

I'm thinking that if I find the third charge, the distance (x) would be no problem.
 
  • #5
Hang on... x = 10 what? What are the units of x?
 
  • #6
the book just says x=10, as in on the x-axis.

it doesn't give specific units...

the answer is 44.4 (no units) so that means that it's 4.44 times farther from -5q than +3q to -5q (10 units)
 
  • #7
You said the charge at x=0 was -q in your OP, not -5q, hence the confusion. I still don't get the value for x as 44.4, though, so I will back down and give way to my betters.
 
  • #8
BTW, you shouldn't need to know the third charge, since if the potential at x=44.4 is zero, there will be no net force regardless of the charge. The potential energy of a unit test charge at distance r is given by E = q/(4*pi*e0*r), where e0 is the permitivity of free space. However, I got x=25 so I'm doing something daft.
 
  • #9
oops..i didnt realize the typo in the first post. i changed it.

am i supposed to use F=kq1q2/r^2?
 
  • #10
Yes, I was being very, very thick. Sorry.

You want to find the value of x at which the force on an arbitrary charge Q is 0.

So, at this point x, the force due to the charge at x=0 is:

F = -5qQ/(4*pi*e0*x^2)

and the force due to the charge at x=10 is:

F = 3qQ/(4*pi*e0*(x-10)^2)

so the total force is:

F = -5qQ/(4*pi*e0*x^2) + 3qQ/(4*pi*e0*(x-10)^2)

and we want F to be 0, so:

3qQ/(4*pi*e0*(x-10)^2) = 5qQ/(4*pi*e0*x^2), so
3x^2 = 5(x-10)^2.

This second part expands to 5x^2 - 100x + 500, so:

3x^2 = 5x^2 - 100x + 500, so
2x^2 - 100r + 500 = 0.

Stick that in the quadratic formula and you have:

x = (-b + root(b^2 - 4ac))/2a
= (100 + root(100^2 - 4*2*500))/4
= 44.4

It's Friday. Hard to think of anything except booze and women.
 
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  • #11
thank you so much!
 
  • #12
You're welcome. You'll notice, of course, I performed two complex mathematical operations on the force due to the charge at x=0, so that it was 5qQ... instead of -5qQ. The first of these two operations is technically known as a 'typo', while the second, more complex one, is called a 'copy and paste error'. However, I've amended it now.
 

1. What is charge and how is it measured?

Charge is a fundamental property of matter that describes the amount of electrical energy an object possesses. It is measured in Coulombs (C) and can be positive or negative.

2. How does charge affect objects?

Objects with the same charge will repel each other, while objects with opposite charge will attract each other. Charge also plays a role in how objects interact with electric and magnetic fields.

3. What is the difference between static and current charge?

Static charge refers to the buildup of excess charge on an object, while current charge refers to the flow of charge through a conductor. Static charge can lead to electric shocks, while current charge is essential for electricity to power our devices.

4. Can charge be created or destroyed?

No, according to the law of conservation of charge, charge cannot be created or destroyed. It can only be transferred from one object to another.

5. How is charge related to voltage and current?

Charge is the product of voltage and current, as determined by Ohm's Law (Q = V x I). This means that the amount of charge present in a circuit is directly proportional to the voltage and current flowing through it.

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