# Work and Voltage

Question 1: Is voltage measured as the amount of work a charge can do as it flows between two points because work is proportional to force? Thus by measuring the amount of work a certain amount of charge is doing as it flows between two points, we are able to indirectly measure the electromotive force acting on that charge?

Question 2: Do we measure electromotive force this way because it is somehow easier to measure the loss of energy of the charge than the force acting on it?

Question 3: Work is equal to Force x Distance. Does this then mean that we could increase voltage by increasing the distance between the two points we are measuring? Obviously not, since this isn't true in practice. So how does distance affect electromotive force, if at all? It seems as if it shouldn't affect it at all if voltage is truly a force.

Please note: I've seen some explanations involving calculus, which I don't know. My math knowledge is only up to pre-calc.

In answer to questions 1 and 2, voltage is defined this way, not measured. Voltage is usually measured by allowing a small current to flow across a resistor, and measuring the current. Look up "voltmeter" on the internet.

In answer to question 3, no, you cannot increase the voltage between two points by increasing the distance between them. Imagine you attach long wires to the ends of a battery and then move the wire's ends away from each other. The voltage between the ends of the wires will not suddenly increase as the ends move. You could try the experiment using a multimeter, a battery, and some pieces of wire if you don't believe that.

The key point is that although the voltage stays constant, the distance changes, so the force exerted on a charged particle between the wire ends must change. The fact that the voltage remains constant while the field strength varies in this and other common situations also explains why we often measure voltages rather than field strengths.

• @ThePhoton - I will copy that useful comment into the answer. – Dusty Jun 29 '18 at 4:45
1. Yes.
2. You are assuming something wrong here. Yes, we can measure the electromotive force as the work done in moving a charge - but we usually don't measure it that way. Much more often it is the other way around; you know your electromotive force, e.g. by a battery, and from that you know the energy in the circuit. An electromotive force is usually what you call the provider of energy to the system.

3. Work equals force time distance, yes, $W=Fd$. In electrical terms this corresponds to voltage equaling the electric field times the distance: $$V=Ed$$ But be careful with such formulas. Changing $d$ does not necessarily change $V$; it may change $E$ instead. Which is exactly the case with e.g. a battery. The voltage is always constant, but reducing the distance for example by moving two wires from each pole close, will increase the electric field strength $E$, which is the force per charge.

if voltage is truly a force.

This is incorrect. Voltage is not a force. It is energy per charge. The term electromotive force is also not a force. It is just a neat phrase, because it seems to be the "driving" force in a circuit. But it isn't a force, it is again just energy per charge, and the word "force" in that term should maybe have been called something else to avoid this confusion.

• If voltage is not a measure of force, then how does it affect the flow of charge? I've heard of the PE gradient explanation, but this seems lacking. In the diffusion of particles from high to low conc. this is DUE to random movement of particles. In the tenedency of an object to move from high to low gravitational PE, this is DUE to the force of grav. What is the force causing the flow of current? – Peter Blood Jun 29 '18 at 19:10
• "What is the force causing the flow of current" That would be an electric force. It starts at the battery. Electrons (and other like charges) repel each other. With many electrons gathered at the negative battery terminal, they really want to move away from there due to this electric repulsion force. If you attached a circuit across the terminals, then the electrons will move into the wire in order to escape the large repulsion. Electrons in the wire are therefore pushed one after another as pearls on a string. The driving forces are always electric repulsion/attraction forces. – Steeven Jun 29 '18 at 20:29
• @PeterBlood We then invent the term electrical potential energy to indicate how much the electrons want to move away. The electrons at the negative terminal feel large repulsion and really want to move to the positive terminal, if they could, since there are no (or less) electrons to repel them there. We therefore say that the negative terminal has a high and the positive a low electrical potential energy. The term voltage is just the difference in potential energy (per charge) - if there is a voltage, then there is a difference, and then the charges want to move due to some force. – Steeven Jun 29 '18 at 20:33