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I've been wrestling with this for a few days (not literally). I got confused because I read in a book that E = - ∇ [itex]\phi[/itex] where E is the electric field and [itex]\phi[/itex] is the scalar potential. However in my notes I had that for a conservative force F = -∇[itex]\phi[/itex]. I got confused because electric force and electric field are not the same thing, but I eventually realised that the [itex]\phi[/itex] in force is potential energy and not potential as it is with the electric field.

A long time ago I recall someone telling me that you could miss out a factor in scalar potential. Is this right? my reasoning was that because potential and potential energy only differ by a constant factor for example q (charge), and if you were dealing with just scalar potential and not potential energy you could remove this factor?

On the enclosed attatchment, they are showing that the line integral for work on a conservative field can be written as difference in potential. It looks like it should be = -3[itex]\int d\phi[/itex] but they just write = -[itex]\int d\phi[/itex], have they missed out the factor of 3?

I'm sorry if what I have said is complete BS, but I wanted to get it cleared up =)

Thanks

A long time ago I recall someone telling me that you could miss out a factor in scalar potential. Is this right? my reasoning was that because potential and potential energy only differ by a constant factor for example q (charge), and if you were dealing with just scalar potential and not potential energy you could remove this factor?

On the enclosed attatchment, they are showing that the line integral for work on a conservative field can be written as difference in potential. It looks like it should be = -3[itex]\int d\phi[/itex] but they just write = -[itex]\int d\phi[/itex], have they missed out the factor of 3?

I'm sorry if what I have said is complete BS, but I wanted to get it cleared up =)

Thanks