Conservation of Electric Energy · 电能守恒
A charge in a field is like a ball on a hill
- Release a ball on a slope and it speeds up, trading height for speed.
- Release a charge in an electric field and it does the same, trading electric potential energy for kinetic.
- The two energies swap, but their total never changes.
- Energy conservation, which we met for gravity, works just as well for charges.
场中的电荷就像山坡上的球
- 在斜坡上松开一个球,它加速,用高度换速度。
- 在电场中松开一个电荷,它做同样的事,用电势能换动能。
- 两种能量互换,但它们的总量从不改变。
- 我们在引力中见过的能量守恒,对电荷同样适用。
PE and KE trade off
- A charge moving through a field converts electric PE into kinetic energy (or back).
- $U + \tfrac12 mv^2 = \text{constant}$ for a charge with no other forces.
- Let a positive charge be repelled: its PE falls and it speeds up.
- Push it against the field: its speed drops and its PE rises.
势能与动能互换
- 在场中运动的电荷把电势能转化为动能(或反过来)。
- 对没有其他力的电荷,$U + \tfrac12 mv^2 =$ 常数。
- 让一个正电荷被排斥:它的 PE 下降、速度加快。
- 逆着场推它:它的速度下降、PE 升高。
As a positive charge is repelled and speeds up, its electric potential energy: · 当正电荷被排斥并加速时，其电势能：
PE falls as it converts into kinetic energy; the total stays constant. · PE下降，转化为动能；总量保持不变。
For a charge with no other forces, electric PE plus ____ energy is constant. · 对于不受其他力作用的电荷，电势能加____能量是恒定的。
$U + \tfrac12 mv^2 = \text{constant}$ — PE and kinetic energy trade off. · $U + \tfrac12 mv^2 = \text{constant}$ — PE和动能相互转化。
Using voltage to find speed
- The energy a charge gains crossing a voltage $\Delta V$ is $W = q\,\Delta V$.
- All of it can become kinetic energy: $q\,\Delta V = \tfrac12 m v^2$.
- This is exactly how particle accelerators speed up electrons and protons.
- Bigger voltage or bigger charge means a faster final speed.
用电压求速度
- 电荷跨过电压 $\Delta V$ 所获得的能量是 $W = q\,\Delta V$。
- 它可以全部变成动能:$q\,\Delta V = \tfrac12 m v^2$。
- 这正是粒子加速器加速电子和质子的方式。
- 更大的电压或更大的电荷意味着更快的末速度。
A $2\ \text{C}$ charge accelerates from rest through $9\ \text{V}$. How much kinetic energy does it gain, in $\text{J}$? · 一个$2\ \text{C}$电荷从静止开始穿过$9\ \text{V}$。它获得了多少动能，单位为$\text{J}$？
$\text{KE} = q\Delta V = 2 \times 9 = 18\ \text{J}$.
Particle accelerators use a voltage to convert electric potential energy into kinetic energy of charges. · 粒子加速器使用电压将电势能转换为电荷的动能。
A charge gains $q\Delta V$ of kinetic energy crossing the voltage — how accelerators work. · 电荷穿过电压获得$q\Delta V$的动能——这就是加速器的工作原理。
The same toolkit as mechanics
- Conservation of energy links the start and end without tracking the messy middle.
- Set total energy at the start equal to total energy at the end, and solve.
- It unifies electricity with all the mechanics energy tools you already know.
- Whenever forces are conservative (gravity, springs, electric), this shortcut works.
与力学相同的工具箱
- 能量守恒把开始和结束联系起来,不必追踪杂乱的中间过程。
- 把开始时的总能量等于结束时的总能量,然后求解。
- 它把电学与你已经熟知的所有力学能量工具统一起来。
- 每当力是保守的(引力、弹簧、电力),这个捷径就有效。
Charge gaining or losing kinetic energy · 电荷获得或损失动能
As a charge moves through a field, energy shifts between kinetic and potential. Sort each case. · 当电荷在电场中移动时，能量在动能和势能之间转换。对每种情况进行排序。
Select all · 所有 true statements about a charge moving freely in an electric field. · 选择所有关于电荷在电场中自由运动的正确陈述。
Energy is conserved (traded, not created); crossing $\Delta V$ transfers $q\Delta V$. · 能量守恒（转化而非创造）；穿过$\Delta V$转移$q\Delta V$。
Conservation of energy applies only when no energy leaks away (no friction or resistance stealing it). In a circuit, resistors turn electrical energy into heat, so there the energy is conserved overall but not stored as kinetic — track where it goes.
能量守恒只在没有能量泄漏时适用(没有摩擦或电阻把它偷走)。在电路中,电阻把电能变成热,所以那里能量总体守恒,但不作为动能储存——要追踪它去了哪里。
In a circuit, why isn't all the electrical energy turned into kinetic energy? · 在电路中，为什么并非所有电能都转化为动能？
Resistors convert electrical energy to heat, so energy is conserved overall but not stored as motion. · 电阻器将电能转化为热，因此总能量守恒，但不是以运动形式储存。
A charge of $q = 2\ \text{C}$ is accelerated from rest through a potential difference of $\Delta V = 9\ \text{V}$. How much kinetic energy does it gain?
- $\text{KE} = q\,\Delta V = 2 \times 9 = 18\ \text{J}$.
All the electric potential energy it loses reappears as kinetic energy.
一个 $q = 2\ \text{C}$ 的电荷从静止经 $\Delta V = 9\ \text{V}$ 的电势差加速。它获得多少动能?
- $\text{KE} = q\,\Delta V = 2 \times 9 = 18\ \text{J}$。
它失去的所有电势能都重新以动能出现。
Conservation of electric energy: a charge trades electric potential energy for kinetic energy with the total unchanged, $U + \tfrac12 mv^2 = \text{constant}$. Crossing a voltage, it gains $W = q\,\Delta V$ — how accelerators work. It is the same energy toolkit as mechanics.
电能守恒:电荷用电势能换动能而总量不变,$U + \tfrac12 mv^2 =$ 常数。跨过电压时,它获得 $W = q\,\Delta V$——加速器就是这样工作的。它与力学是同一套能量工具。