Electrostatic Fields, Lecture notes of Physics

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Electric Fields
23.1 Properties of Electric Charges
โ€ขElectrostatic is the study of electric
charges which are not moving.
โ€ขTypes of Charge: There are two types of electric
charges, arbitrarily called positive and negative.
โ€ขThe net charge of a closed system never
changes.
โ€ขThe net charge is found by adding the charges
arithmetically.
โ€ขRubbing certain electrically neutral objects
together (the first material used was amber and
fabric), tends to cause these objects to attract or
repel small objects.
โ€ขThese objects are said to be charged.
โ€ขIf an object contains equal numbers of positive
and negative charges, it is electrically neutral.
โ€ขAfter separation, the negative charges and
positive charges are found to attract each other.
โ€ขOn the other hand positive charges exert a
repulsive force on one another, the same as
negative charges. These results can be
summarized as : unlike charges attract and like
charges repel.
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Electric Fields

23.1 Properties of Electric Charges

โ€ข Electrostatic is the study of electric

charges which are not moving.

  • Types of Charge: There are two types of electric

charges, arbitrarily called positive and negative.

  • The net charge of a closed system never

changes.

  • The net charge is found by adding the charges

arithmetically.

  • Rubbing certain electrically neutral objects

together (the first material used was amber and

fabric), tends to cause these objects to attract or

repel small objects.

  • These objects are said to be charged.
  • If an object contains equal numbers of positive

and negative charges, it is electrically neutral.

  • After separation, the negative charges and

positive charges are found to attract each other.

  • On the other hand positive charges exert a

repulsive force on one another, the same as

negative charges. These results can be

summarized as : unlike charges attract and like

charges repel.

  • The net amount of electric charge produced in any

process is zero.

  • In other words: in any process, electric charge can

not be created or destroyed, however it can be

transferred from one object to another.

  • During the past century, the negative charges

have been shown to be carried by particles which

are now called electrons, while the positive

charge carriers are known as protons.

  • In 1909, Robert Millikan (1868 โ€“ 1953)

discovered that electric charge always occurs as

some integral multiple of a fundamental amount

charge e.

  • The charge carried by an electron is โ€“ e and the

charge carried by a proton is +e, where e is the

elementary charge.

e ๏€ฝ 1. 602 ๏‚ด 10 ๏€ญ^19 C

  • Electrons are bound to atoms and molecules, but

how tightly bound varies dramatically.

  • In some material, the electrons are free to move,

these are called conductors.

  • In other materials, the electrons are much more

tightly bound to the atoms or molecules, these are

called insulators.

  • Materials that are intermediate between

conductors and insulators are called

semiconductors.

Charging by Rubbing

  • Some insulating materials, when rubbed together, result in a net charge on each object.

23.3 Coulombโ€™s Law

  • States that two point charges exert a force F on one another, that is 23.3 Coulombโ€™s Law
  • States that two point charges exert a force F on one another, that is
  • States that two point charges exert a force F on one

another, that is

2 2 9 2 1 2 2 1 2

C

N m

k

r

q q

F k

r

F

F qq

e e e e

  • This value of k is valid only in vacuum.
  • is the permittivity of free space.

๏ฐ๏ฅ

ke ๏€ฝ

๏ฅ 0 2 2 12

0 8.^8510

Nm

C

k

๏€ฝ ๏€ฝ ๏‚ด^ ๏€ญ

๏ฐ ๏ฅ Example 23. The Hydrogen Atom

  • The electron and proton of a hydrogen atom are separated (on the average) by a distance of approximately 5. 3 ร— 10 โˆ’^11 m. Find the magnitude of the electric force and the gravitational force between the two particles.
  • ๐‘˜๐‘’ = 8. 99 ร— 109 N ๐‘š^2 /๐ถ^2 ,๐‘’ = 1. 602 ร— 10 โˆ’^19 ๐ถ
  • ๐บ = 6. 67 ร— 10 โˆ’^11 ๐‘ ๐‘š^2 /๐‘˜๐‘”^2 , ๐‘š๐‘’ = 9. 11 ร— 10 โˆ’^31 ๐‘š๐‘ = 1. 67 ร— 10 โˆ’^27 Example 23. Find the Resultant Force
  • Consider three point charges located at the corners of a right triangle as shown in Figure 23.7, where ๐‘ž 1 = ๐‘ž 3 = 5. 00 ๐œ‡๐ถ, ๐‘ž 2 = โˆ’ 2. 00 ๐œ‡๐ถ, and ๐‘Ž =
  1. 100 ๐‘š. Find the resultant force exerted on ๐‘ž 3. Example 23. Where is the Net Force Zero?
  • Three point charges lies along the ๐‘ฅ axis as shown in Figure 23.8. The positive charge ๐‘ž 1 = 15. 0 ๐œ‡๐ถ is at ๐‘ฅ = 2. 00 ๐‘š, the positive charge ๐‘ž 2 = 6. 00 ๐œ‡๐ถ is at the origin, and the net force acting on ๐‘ž 3 is zero. What is the ๐‘ฅ coordinate of ๐‘ž 3. Example 23. Find the Charge on the Spheres
  • Two identical small charged spheres, each having a mass 3. 00 ร— 10 โˆ’^2 ๐‘˜๐‘” , hang in equilibrium as shown in Figure 23.9a. The length ๐ฟ of each string is 0. 150 ๐‘š, and the angle ๐œƒ is 5. 00 ยฐ. Find the magnitude of the charge on each sphere.