Neutralizing Forces Between Electric Charges

In summary, the third charge must be placed between the charges, to the left of the origin, to experience a net force of zero.
  • #1
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Homework Statement


Consider a charge of +2.0 µC placed at the origin of an X-Y co-ordinate system and a charge of -4.0 µC placed 40.0 cm to the right. Where must a third charge be placed – between the charges, to the left of the origin, or beyond the second charge – to experience a net force of zero? Argue your case qualitatively without working out a solution. Consider both positive and negative charges.

Homework Equations


[tex]F=k((q1*q2)/r^{2})[/tex]

The Attempt at a Solution


Wouldn't you have to place the third one directly in the middle of the two charges? because you will then have the left side of the third one being positive and the right side of the third one being negative, therefore canceling out to zero, and the opposite would apply for a negative third charge...

But I'm not sure that i am correct with my reasoning...
 
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  • #2
Say the 3rd charge is positive. If you put the 3rd charge between the first two, the first charge (A) will push it to the right and the second charge (B) will attract it to the right. The two forces to the right do not cancel - they add.

Think about the directions of the two forces in the other two possible positions and you'll find the correct answer.

then have the left side of the third one being positive and the right side of the third one being negative
It sounds like you are thinking of induced charge separation in the 3rd charge. It actually will be the other way round with some positive charge being attracted to the negative charge (B) on the right and repelled by (A) on the left. So the right side will be more positive due to induction. This will partly cancel out because the left side will be attracted to A more strongly than the right side will be repelled by A while the opposite is true for its interaction with B. But the bottom line on induction is that we don't know how it compares in strength with the basic force due to the charge on C. It will be easily overwhelmed by the net charge on C unless that is very small (C is almost neutral). If it is neutral, the force due to induced charge separation will still be to the right in your proposed solution because the positive charge on the right side will be more strongly attracted to the larger B charge than the left side is to the smaller A charge.
 
  • #3
Delphi51 said:
Say the 3rd charge is positive. If you put the 3rd charge between the first two, the first charge (A) will push it to the right and the second charge (B) will attract it to the right. The two forces to the right do not cancel - they add.

Think about the directions of the two forces in the other two possible positions and you'll find the correct answer.


It sounds like you are thinking of induced charge separation in the 3rd charge. It actually will be the other way round with some positive charge being attracted to the negative charge (B) on the right and repelled by (A) on the left. So the right side will be more positive due to induction. This will partly cancel out because the left side will be attracted to A more strongly than the right side will be repelled by A while the opposite is true for its interaction with B. But the bottom line on induction is that we don't know how it compares in strength with the basic force due to the charge on C. It will be easily overwhelmed by the net charge on C unless that is very small (C is almost neutral). If it is neutral, the force due to induced charge separation will still be to the right in your proposed solution because the positive charge on the right side will be more strongly attracted to the larger B charge than the left side is to the smaller A charge.

Hey, I'm somewhat confused now... Don't you just add the forces to find the net acting on the third?
 
  • #4
Yes. Forget about the induced charge separation.
 
  • #5
I'm still not sure about this question.. because it says to not work the problem out.. would I just use repel/attract theory... :confused:

thanks in advance
 

What is net force on electric charges?

The net force on electric charges is the overall force acting on an object due to the presence of multiple electric charges. It takes into account the direction and magnitude of each individual force acting on the charges.

How is net force on electric charges calculated?

The net force on electric charges is calculated by adding up all the individual forces acting on the charges. This can be done using vector addition, taking into account the direction and magnitude of each force.

What factors affect the net force on electric charges?

The net force on electric charges is affected by the distance between the charges, the magnitude of the charges, and the medium in which the charges are located. It is also affected by the presence of other electrically charged objects in the vicinity.

Can the net force on electric charges be zero?

Yes, the net force on electric charges can be zero if the individual forces acting on the charges cancel each other out. This can happen if the charges are equal in magnitude and opposite in direction, or if the distance between the charges is large enough.

How does the net force on electric charges affect the motion of an object?

The net force on electric charges can cause an object to accelerate or experience a change in motion. If the net force is zero, the object will remain at rest or continue moving at a constant velocity. If the net force is non-zero, the object's motion will change in the direction of the net force.

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