Point Charge Potential

The electric potential (voltage) at any point in space produced by a point charge Q is given by the expression below. It is the electric potential energy per unit charge and as such is a characteristic of the electric influence at that point in space. Since it is a scalar quantity, the potential from multiple point charges is just the sum of the point charge potentials of the individual charges and can be extended to calculate the potential from a continuous charge distribution.

Show 显示 k = Coulomb's constant k = 库仑常数

Voltage = k x charge/radius At a distance r = x10^ m from a charge Q = x10^ C the voltage is V = x10^ volts. Enter data, then click on the quantity you wish to calculate in the active formula above. Unspecified parameters will default to 1, but all values may be changed. 输入数据，然后点击上方交互式公式中您希望计算的量。未指定的参数将默认为1，但所有值都可以更改。 电压 = k * 电荷 / 半径。在距离 Q = x10^ C 的电荷 x10^ m 处，电压为 V = x10^ 伏特。 中文译文中的待填/计算数值依次对应：1：rb 2：rp 3：qb 4：qp 5：vb 6：vp。实际数值以上方原输入框为准。

Point Charge Potential

The potential (voltage) of a point charge can be evaluated by calculating the work necessary to bring a test charge q in from an infinite distance to some distance r. The zero of potential is chosen at infinity.

Considering a radial path from a to b, the work done by the Coulomb force is obtained from a line integral which in this case becomes just a polynomial integral since we are moving along a straight radial line: The change in potential is the work done per unit charge against the Coulomb force, so 考虑从a到b的径向路径，库仑力所做的功可通过一条线积分得到，而在这种情况下，由于我们沿着一条直线径向移动，该积分就简化为一个多项式积分：电势的变化是克服库仑力每单位电荷所做的功，因此

For a positive charge q, the Coulomb force does positive work in moving it from a to b, so that represents a drop in potential energy.