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The potential difference between the ends of a conductor is called voltage.

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Q: Define the 'potential difference between the ends of a conductor'?
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Define voltage in terms of electric potential energy and charge?

When unlike charges are moved farther apart, they gain electrical potential energy. Electrical potential difference is the change in potential energy per coulomb of charge. Voltage is the common name for electrical potential difference and is measured in volts (V). Electrical energy depends on the amount of charge and voltage. Electrochemical cells, or batteries, are a common source of voltage. We use voltmeters to measure potential difference. :)


Is it possible for a system to have negative potential energy?

Yes. Potential energy can't be specified in absolute terms; you have to arbitrarily define a reference point. For the case of gravitation, any object below the reference point would have negative potential energy. What matters is not the number assigned to the potential energy, but the difference - this difference would be the same, even if you change your reference level.


Why does an object sitting on top of a ledge have potential energy?

Whether it has (gravitational) potential energy or not depends on what level you (arbitrarily) define as zero. If you define the bottom of the ledge as the "zero" level, then the top of the ledge will have positive energy. If you define the top of the ledge as the "zero" level, then the object on the top of the ledge will have zero potential energy (and at the bottom of the ledge it will have negative potential energy). In any case, at the top of a ledge, an object will have more potential energy than at the bottom of the ledge, because it requires work to push the object up; also, in principle the potential energy can be recovered (converted to some other type of energy) if the object falls down.


Can energy be in negative?

It might, depending on how you define it. Especially in the case of gravitational potential energy, the "zero level" or "base level" is arbitrary; you might define the base level as ground level, for instance. In that case, any object above ground level has a positive potential energy, and any object below ground level has a negative potential energy. Ultimately, what matters is not how much potential energy an object "really has" - it is really hard to define or ascertain this - rather, what matters is how much the energy CHANGES from one position to another. The case is similar with voltages, which are related to potential energy in an electric field.

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Why it is not correct to say that the potential difference is the work done in moving charge between the points concerned?

Voltage is defined as potential difference (units of volts). Work is equivalent to power (over time), and its' unit is joules. Power is equivalent to the potential difference times the current flow. Without current flow, there is no power, so it is incorrect to define potential difference as work. What I think you're implying is potential energy and potential difference are the same: Potential energy of a rock can be increased by raising the rock into the air. The increase of potential energy of the rock is equivalent to the real work done to raise it higher into the air. This is a true statement. Potential energy (joules) and potential difference (volts) are not equivalent, though, since potential differenence is not defined as work.


Why it is not correct to say that potential difference is the work done in moving unit charge between the point concerned?

Voltage is defined as potential difference (units of volts). Work is equivalent to power (over time), and its' unit is joules. Power is equivalent to the potential difference times the current flow. Without current flow, there is no power, so it is incorrect to define potential difference as work. What I think you're implying is potential energy and potential difference are the same: Potential energy of a rock can be increased by raising the rock into the air. The increase of potential energy of the rock is equivalent to the real work done to raise it higher into the air. This is a true statement. Potential energy (joules) and potential difference (volts) are not equivalent, though, since potential differenence is not defined as work.


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