Electrostatic energy of three charges

[Vibhor]

Homework Statement

Two equal charges of magnitude Q each are placed at a distance d apart .Their electrostatic energy is E. A third charge -Q/2 is brought midway between these two charges .The electrostatic energy of the system is now

A) -2E
B) -E
C) 0
D) E

Homework Equations

EPE = kq₁q₂/r

The Attempt at a Solution

[/B]
The question is quite simple and I have correctly found the answer which is -E i.e option B).

Now what is puzzling me is the signifance of negative electrostatic potential energy of this configuration . By definition of EPE , since energy of this configuration is negative then this means that when a unit test charge is brought from infinity towards the configuration, it experiences an attractive force .But from a far off point , the configuration should look like a net positive charge .Thus , configuration of these charges should repel test charge .

What is the significance of minus sign in the EPE of this configuration ?

Thanks

 

[vela]

By definition of EPE, since energy of this configuration is negative then this means that when a unit test charge is brought from infinity towards the configuration, it experiences an attractive force.

Are you sure about this?

 

[Vibhor]

Are you sure about this?

I might be wrong . EPE is electric potential per unit charge . Electric potential is work done in bringing a unit positive charge from infinity to a point . Since EPE is negative ,negative work is done , in which case the force is attractive from the configuration .

Please explain the mistake in my reasoning .

 

[ehild]

I might be wrong . EPE is electric potential per unit charge . Electric potential is work done in bringing a unit positive charge from infinity to a point . Since EPE is negative ,negative work is done , in which case the force is attractive from the configuration .

Please explain the mistake in my reasoning .

You confuse potential energy of a configuration with the potential around a configuration. The potential at a point P is the potential energy of a unit positive charge placed at that point. In this case, it can be both positive and negative. Far away, it is positive. Close enough to the negative charge, it is negative.
The potential energy of the configuration is equal to the work needed to make it. Negative energy means that energy is released when the three charges are brought into the positions given.

 

[Vibhor]

Negative energy means that energy is released when the three charges are brought into the positions given.

You are right .

In what manner is energy released when the charges are brought to their positions ?

 

[ehild]

You confuse potential energy of a configuration with the potential around a configuration. The potential at a point P is the potential energy of a unit positive charge placed at that point. In this case, it can be both positive and negative. Far away, it is positive. Close enough to the negative charge, it is negative.
The potential energy of the configuration is equal to the work needed to make it.

You are right .

In what manner is energy released when the charges are brought to their positions ?

The charge is attribute of material bodies. So those charges can be charged little balls, for example. If you fix the two positive ones, and release the negative one far away, along the symmetry axis of the other two, it will move towards the positive ones by itself, and the kinetic energy increases during its journey, When it is at d/2 position you catch it and fix it, but the KE is used up somehow. For example, you can stop it by a spring. Or it will hit a hole in your hand :)

 

[Vibhor]

Thanks

 

[David Lewis]

The potential at a point P is the potential energy of a unit positive charge placed at that point.

In the problem statement, does electrostatic energy refer to the energy stored in the system, or the voltage?

I think the term "potential" may signify either potential energy or potential difference (voltage), depending on the context.

 

[SammyS]

In the problem statement, does electrostatic energy refer to the energy stored in the system, or the voltage?

Yes !

Energy stored in the system.