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John Rennie
John Rennie
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The potential energy is the work done on the unit charge as it is moved from $\infty$ to $r$. That is, suppose you are pushing the charge inwards, then the change in PE is the work you do. That means the force we need to calculate the work is directed in the $-r$ direction because it is the inwards force that you are exerting on the charge.

The rationale for this is that if the PE increases that means the energy of the system has increased, and that means energy must have been added to the system from an external source. In this case that external source is you, and the energy added to the system is the work that you are doing on it.

What you have calculated is the work done by the electric field, not the work done by an external agent onon the field. The work done by the field is indeed negative, which means the energy of the electric field is increasing.

Understanding the sign of work is notoriously confusing even for those of us who have been physicists all our life. The approach I take is to look at how the energy is moving. If the PE of a system is increasing then energy must be added to the system from an external source. Conversely if the PE is decreasing then the system must be transferring energy from the system to some external sink.

The potential energy is the work done on the unit charge as it is moved from $\infty$ to $r$. That is, suppose you are pushing the charge inwards, then the change in PE is the work you do. That means the force we need to calculate the work is directed in the $-r$ direction because it is the inwards force that you are exerting on the charge.

The rationale for this is that if the PE increases that means the energy of the system has increased, and that means energy must have been added to the system from an external source. In this case that external source is you, and the energy added to the system is the work that you are doing on it.

What you have calculated is the work done by the electric field, not the work done by an external agent on the field. The work done by the field is indeed negative, which means the energy of the electric field is increasing.

Understanding the sign of work is notoriously confusing even for those of us who have been physicists all our life. The approach I take is to look at how the energy is moving. If the PE of a system is increasing then energy must be added to the system from an external source. Conversely if the PE is decreasing then the system must be transferring energy from the system to some external sink.

The potential energy is the work done on the unit charge as it is moved from $\infty$ to $r$. That is, suppose you are pushing the charge inwards, then the change in PE is the work you do. That means the force we need to calculate the work is directed in the $-r$ direction because it is the inwards force that you are exerting on the charge.

The rationale for this is that if the PE increases that means the energy of the system has increased, and that means energy must have been added to the system from an external source. In this case that external source is you, and the energy added to the system is the work that you are doing on it.

What you have calculated is the work done by the electric field, not the work done by an external agent on the field. The work done by the field is indeed negative, which means the energy of the electric field is increasing.

Understanding the sign of work is notoriously confusing even for those of us who have been physicists all our life. The approach I take is to look at how the energy is moving. If the PE of a system is increasing then energy must be added to the system from an external source. Conversely if the PE is decreasing then the system must be transferring energy from the system to some external sink.

Source Link
John Rennie
John Rennie
  • 358k
  • 127
  • 769
  • 1.1k

The potential energy is the work done on the unit charge as it is moved from $\infty$ to $r$. That is, suppose you are pushing the charge inwards, then the change in PE is the work you do. That means the force we need to calculate the work is directed in the $-r$ direction because it is the inwards force that you are exerting on the charge.

The rationale for this is that if the PE increases that means the energy of the system has increased, and that means energy must have been added to the system from an external source. In this case that external source is you, and the energy added to the system is the work that you are doing on it.

What you have calculated is the work done by the electric field, not the work done by an external agent on the field. The work done by the field is indeed negative, which means the energy of the electric field is increasing.

Understanding the sign of work is notoriously confusing even for those of us who have been physicists all our life. The approach I take is to look at how the energy is moving. If the PE of a system is increasing then energy must be added to the system from an external source. Conversely if the PE is decreasing then the system must be transferring energy from the system to some external sink.