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Unfortuneately, this definition has a caveat. In order for a potential to exist ∇×E must be zero. |
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Unfortuneately, this definition has a caveat. In order for a potential to exist ∇×E must be zero. Whenever the charges are stationary, however, this condition will be met, and finding the field of a moving charge simply requires a relativistic transform of the electric field. |
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where q is the point charges charge, r is the position, and rq is the position of the point charge. The potential for a general distribution of charge ends up being: |
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where q is the point charge's charge, r is the position, and rq is the position of the point charge. The potential for a general distribution of charge ends up being: |
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Note well that φ is a scalar, which means that it will add to other potential fields as a scalar. The fact that the electric potential is a scalar proves to be extremely useful when calculating the electric field because, from the definition of the electric potential: |
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Note well that φ is a scalar, which means that it will add to other potential fields as a scalar. This makes makes it relatively easy to break complex problems down in to simple parts and add their potentials. Getting the electric field from the potential is just a matter of taking the definition of φ backwards: |
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which is much easier to calculate. It is so much easier to calculate that the electric field is more frequently expressed in V/m (volts per meter) than in Newtons per coulomb. |
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Calculating E from φ is so much easier than calculating E from the charge density that the electric field is more frequently expressed in V/m (volts per meter) than in Newtons per coulomb. |
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