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EMF 与电位差

1870

James Clerk Maxwell

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Electromotive force (EMF) and electric potential difference (voltage) are distinct concepts, though both are measured in volts. EMF is the work per unit charge done by a non-conservative force (e.g., chemical reaction, changing magnetic field) to move charge within a source. Potential difference is the work per unit charge done by the conservative electrostatic field between two points.

The core difference between EMF and potential difference lies in the nature of the underlying fields. The electrostatic field ([latex]\mathbf{E}_{c}[/latex]), created by static charges, is conservative. This means the work it does on a charge moving around any 闭环 is zero: [latex]\oint \mathbf{E}_{c} \cdot d\mathbf{l} = 0[/latex]. The potential difference, or voltage, between two points is the line integral of this conservative field, [latex]V = -\int \mathbf{E}_{c} \cdot d\mathbf{l}[/latex]. In contrast, an EMF source generates a non-conservative field or “impressed field” ([latex]\mathbf{E}_{nc}[/latex]). This field does non-zero work on a charge around a closed loop: [latex]\mathcal{E} = \oint \mathbf{E}_{nc} \cdot d\mathbf{l} \neq 0[/latex].

In a simple DC circuit with a battery, the battery provides the EMF. Inside the battery, the non-conservative chemical forces move positive charges from the negative to the positive terminal, against the opposing conservative electrostatic field. This “uphill” journey is where the EMF does its work. Outside the battery, in the external circuit, the charges move “downhill” from the positive to the negative terminal, driven by the conservative electrostatic field. The potential drop across the external resistor is equal to the EMF minus the potential drop across the battery’s internal resistance. Thus, EMF is the cause of the sustained current, while potential difference is the measure of energy dissipated per unit charge in a part of the circuit.