Force as charges are brought closer?

[September24]

I thought this was a simple concept but I'm getting a little confused.


F=kqq/r^2


Generally, if you bring two charges together, the force increases. However, I've been looking at electrostatic equation lately in a "quantitative" manner and its REALLY confusing me.

What if the charges are opposite. If you bring a negative and positive charge closer. The force would end up being "negative" and get bigger. Since its getting more negative, does that mean that if you bring a positive and negative charge closer, the force gets smaller (more negative)?

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[September24]

Follow up question. If you put a positive charge in an electric field. As it goes in the direction of the field, its PE goes down. Therefore, since it's U goes down, is work done ON it by the E field. It gains KE but its technically decreasing the PE. You need to do work to move a proton against a electric field, but would you go work to push it in the same direction as the field. This concept still confuses me.

 

[BrawnsNBrain]

I think I might be confused by your question but here's what I took from it.

The positive or negative force just refers to if it's an attractive or repulsive force.

If a the charge is moving in the natural direction of the E-field then no work is required to move it. Remember, if PE decreases but KE increases by the same magnitude, energy is still conserved

 

[Paean1]

1)As Brawns said, the +/- just refer to direction of the force.

2)Electrostatic force is a conservative force. When a conservative force (e.g. gravitational, spring, etc.) does net work the mechanical energy is conserved (PE+KE=constant) but the energy changes form--from potential to kinetic or vice versa. So, yes the electric field does positive work on the charge but it does not add energy to the system, it only converts it--which is the definition of work for a conservative force.

If you pushed the positive charge in the same direction as the electric field (applied a force to the charge) then you would be doing work. If you pushed the positive charge against the direction of the electric field you are also doing work. The work you do adds or subtracts energy from the system because the force you apply is non-conservative.

 

[September24]

The reason I'm so fixated on this work stuff is mainly due to sign convention. I'm usually told that if positive work is done on an object , it gains energy. With a conservative force, sign convention confuses me

 

[Paean1]

If the conservative force does negative work then the PE has increased (think of moving an apple up 10m, the force of gravity on the apple is downward but the direction of movement is upward, so based on W=Fdcos(theta) gravity does negative work and the PE increases). If the conservative force does positive work then the KE has increased (if the apple is now released from 10m, the force of gravity is downward and the direction of movement is downward, so based on W=Fdcos(theta) the gravity does positive work and KE increases). The concept is the same for electrostatic forces.

 

[September24]

Oh okay. With gravitational force, it seems pretty simple. If it's in the direction of the force, then work is positive.

But how about an electrostatic force. You said it's the same but it doesn't seem like it to me conceptually. An electric field will move a proton from high to low voltage. However, we need to do positive work to move a proton against an electric field. If this happens, the proton goes to a high potential and gains PE. In this case , doing positive work makes the proton gain PE?

Or maybe I'm wrong because in my example, I'm not talking about the conservative force. "We" (another force) does positive work to move a proton against the field. But the conservative electric field force does negative work as a proton is moved against it? Is this right?

I'm sorry, work sign convention has always been an area of weakness and I've done countless problems on it. Somehow as soon as I thought I figured it out, I get confused again

 

[Paean1]

Yeah exactly--"we" refers to our force on the charge, not the conservative force (electrostatic in this case) which is doing negative work.