# 物理 energy of electron, radius

以下是我不明白的問題：

1. 為甚麼 electric potential energy 是 negative？我在網上找過資料，它們說 electric potential energy at infinity 是 definded 0，但是為甚麼要這樣定義？

2. 書中有一條問題：

A negatively charged particle A orbits around a fixed positively charged particle B.

The charges of A and B are -Qa and Qb respectively, and their masses are Ma and Mb. Given that the radius of the orbit of A is r

a) Find the Kinetic energy of A

ANS : QaQb/ (8πεr)

b) What happens to A if its Kinetic energy decreases.

Ans: By the equation in (a), when K.E. decreases, r increases.i.e. the radius of the orbit of A increases.

But，

一開始 electric force = 向心力

但假如KE decrease， electric force > 所需的向心力，所以應該會 spiral inwards

r 應該會 decrease

另外，Total energy of A = - QaQb/ (8πεr)

當KE decreases， Total energy decreases，所以 r 應該會decrease

這些推論是否正確？假如正確，那為甚麼與書的答案有矛盾？

希望各位幫忙！

Thanks For your answer !!!

But there's still something that I don't understand.

1. why the KE of particle A would increase when r decreases ?

Consider the circular motion, when radius decreases, the linear speed should decrease,which means KE should decrease.

2. Also, I understand that a decrease of KE is resulted by an increase of potential energy if total energy remains constant

But then, when KE decreases, PE increases, total energy remains constant

according to the equation of total energy = - QaQb/ (8πεr), r should remain unchanged. Hence the total enery seem not to be constant.

### 1 個解答

- 天同Lv 75 年前最愛解答
1. This follows the definition in mechanics. Potential energy for repulsice force is +ve and for attractive force is -ve. The reason behind is that wok needs to be done when two +ve charges come near to each other, and -ve work is done (i.e. energy is being released) for charges of opposite signs come together.

2. Should your argment is correct (i.e. r decreases), the KE of particle A would increase. This contradicts to what is asked in the question that what happen when KE of A decreases.

This is simple mechanics, given the total energy remains constant, a decrease of KE results in an increase of potential energy (PE) and vice versa.

2015-07-01 12:31:35 補充：

Just to amend the last paragraph to read as:

This is simple mechanics, given the total energy remains constant, a decrease of KE is resulted by an increase of potential energy (PE) and vice versa.

2015-07-01 20:53:53 補充：

Your suppl questions:

1. Remember that particle A is under an attractive force (given by particle B). At a given orbit, there is a balance of electrical force and centripetal force, thus the KE and PE is fixed....

2015-07-01 20:54:34 補充：

(cont'd)...

Should the speed of A decrease (by whatever means), particle A will be pulled down by the electrical force and hence increase its speed, leading to an increase of KE (this is a result of work done by the electrical attractive force).

2015-07-01 21:02:08 補充：

2. In a circular motion under an attractive field, the higher the orbit, the more is the total energy. But the same principle holds...

2015-07-01 21:02:49 補充：

(cont'd)...

When particle A changes its orbit from a lower to a higher one, work needs to be done againt the attractive force between the two charges. This decreases the KE of the particle.