Electric potential energy

Electric Potential Energy

电势能

Potential energy can be defined as the capacity for doing work which arises from position or configuration. In the electrical case, a charge will exert a force on any other charge and potential energy arises from any collection of charges. For example, if a positive charge Q is fixed at some point in space, any other positive charge which is brought close to it will experience a repulsive force and will therefore have potential energy. The potential energy of a test charge q in the vicinity of this source charge will be:

势能可以定义为由于位置或配置而产生的做功能力。在电学情况下，一个电荷会对另一个电荷施加力，而电荷的集合会产生势能。例如，如果一个正电荷Q固定在空间中的某点，任何其他正电荷靠近它时都会受到排斥力的作用，因此会具有势能。在该源电荷附近的一个测试电荷q的势能为：

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where k is Coulomb's constant.

其中k是库仑常数。

In electricity, it is usually more convenient to use the electric potential energy per unit charge, just called electric potential or voltage.

在电学中，通常更方便使用单位电荷的电势能，简称电势或电压。

Application:Coulomb barrier for nuclear fusion

应用：核融合的库仑障壁

Energy in electron volts

电子伏特中的能量

Zero Potential

零电势

The nature of potential is that the zero point is arbitrary; it can be set like the origin of a coordinate system. That is not to say that it is insignificant; once the zero of potential is set, then every value of potential is measured with respect to that zero. Another way of saying it is that it is the change in potential which has physical significance. The zero of electric potential (voltage) is set for convenience, but there is usually some physical or geometric logic to the choice of the zero point. For a single point charge or localized collection of charges, it is logical to set the zero point at infinity. But for an infinite line charge, that is not a logical choice, since the local values of potential would go to infinity. For practical electrical circuits, the earth or ground potential is usually taken to be zero and everything is referenced to the earth.

电势的性质是零点是任意的；它可以像坐标系的原点一样设定。这并不意味着它不重要；一旦零点被设定，那么所有电势的值都是相对于该零点来测量的。另一种说法是，具有物理意义的是电势的变化，而不是电势本身。电势（电压）的零点是出于方便而设定的，但通常有一些物理或几何逻辑来决定零点的选择。对于单个点电荷或局部化的电荷集合，将零点设在无穷远处是合理的。但对于无限长的线电荷，这种选择并不合理，因为局部的电势值会趋于无穷大。对于实际的电气电路，通常将地或接地电势取为零，所有东西都是以地为参考的。

Potential Reference at Infinity

无限远处的势参考点

The general expression for the electric potential as a result of a point charge Q can be obtained by referencing to a zero of potential at infinity. The expression for the potential difference is:

电势由点电荷Q产生的通用表达式可通过参考无穷远处的电势零点来获得。电势差的表达式为：

Taking the limit as r_b→∞ gives simply
当 r b → ∞ 时， simply 给出的只是

for any arbitrary value of r. The choice of potential equal to zero at infinity is an arbitrary one, but is logical in this case because the electric field and force approach zero there. The electric potential energy for a charge q at r is then

对于任意的r值。将势能在无穷远处取零是一个任意的选择，但在这种情况下是合理的，因为电场和力在那裡趋于零。因此，对于位于r处的电荷q，其电势能为

where k is Coulomb's constant.

其中k是库仑常数。