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Bob D
Bob D
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Can work be 0 but the potential energy still increase?

The net work on a charge can be zero while the potential energy of the system of charges increases.

But since the integral of work from the force I exert and the electric force cancel out, there is no work.

There is no net work done.

Per the work energy theorem, the net work done on an object equals its change in kinetic energy. Since there was no change in kinetic energy, the net work done is zero. You did positive work since your force was in the direction of the displacement, while the electric field did an equal amount of negative work, since its force was opposite to the direction of the displacement, for a net work of zero. The end result is the electric field took the energy you gave the charge and stored it as electrical potential energy in the two charge system.

The gravity analogy is lifting an object at constant velocity from point A to point B where the vertical distance between A and B is $h$ and the force of gravity is constant. The change in KE is zero but there is an increase in gravitational potential energy of $mgh$ of the Earth-object system.

Keep in mind that potential energy is a system property. Neither the single negative charge nor the single object being lifted owns the potential energy. In the case of electrical potential energy, it belongs to the configuration of charges. In the case of gravitational potential energy, it belongs to the configuration of gravitating bodies.

Hope this helps.

Can work be 0 but the potential energy still increase?

The net work on a charge can be zero while the potential energy of the system of charges increases.

But since the integral of work from the force I exert and the electric force cancel out, there is no work.

There is no net work done.

Per the work energy theorem, the net work done on an object equals its change in kinetic energy. Since there was no change in kinetic energy, the net work done is zero. You did positive work since your force was in the direction of the displacement, while the electric field did an equal amount of negative work, since its force was opposite to the direction of the displacement, for a net work of zero. The end result is the electric field took the energy you gave the charge and stored it as electrical potential energy in the two charge system.

The gravity analogy is lifting an object at constant velocity from point A to point B where the vertical distance is $h$ and the force of gravity is constant. The change in KE is zero but there is an increase in gravitational potential energy of $mgh$ of the Earth-object system.

Hope this helps.

Can work be 0 but the potential energy still increase?

The net work on a charge can be zero while the potential energy of the system of charges increases.

But since the integral of work from the force I exert and the electric force cancel out, there is no work.

There is no net work done.

Per the work energy theorem, the net work done on an object equals its change in kinetic energy. Since there was no change in kinetic energy, the net work done is zero. You did positive work since your force was in the direction of the displacement, while the electric field did an equal amount of negative work, since its force was opposite to the direction of the displacement, for a net work of zero. The end result is the electric field took the energy you gave the charge and stored it as electrical potential energy in the two charge system.

The gravity analogy is lifting an object at constant velocity from point A to point B where the vertical distance between A and B is $h$ and the force of gravity is constant. The change in KE is zero but there is an increase in gravitational potential energy of $mgh$ of the Earth-object system.

Keep in mind that potential energy is a system property. Neither the single negative charge nor the single object being lifted owns the potential energy. In the case of electrical potential energy, it belongs to the configuration of charges. In the case of gravitational potential energy, it belongs to the configuration of gravitating bodies.

Hope this helps.

Source Link
Bob D
Bob D
  • 77.9k
  • 6
  • 58
  • 152

Can work be 0 but the potential energy still increase?

The net work on a charge can be zero while the potential energy of the system of charges increases.

But since the integral of work from the force I exert and the electric force cancel out, there is no work.

There is no net work done.

Per the work energy theorem, the net work done on an object equals its change in kinetic energy. Since there was no change in kinetic energy, the net work done is zero. You did positive work since your force was in the direction of the displacement, while the electric field did an equal amount of negative work, since its force was opposite to the direction of the displacement, for a net work of zero. The end result is the electric field took the energy you gave the charge and stored it as electrical potential energy in the two charge system.

The gravity analogy is lifting an object at constant velocity from point A to point B where the vertical distance is $h$ and the force of gravity is constant. The change in KE is zero but there is an increase in gravitational potential energy of $mgh$ of the Earth-object system.

Hope this helps.