Electrostatics - Applied Physics - Lecture Slides, Slides of Applied Chemistry

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Electrostatics

• Electrostatics is the branch of

electromagnetics dealing with the

effects of electric charges at rest.

• The fundamental law of

electrostatics is Coulomb’s law.

Electric Charge

• Electrical phenomena caused by friction are part of our everyday lives, and can be understood in terms of electrical charge.
• The effects of electrical charge can be observed in the attraction/repulsion of various objects when “charged.”
• Charge comes in two varieties called “positive” and “negative.”

Electric Charge

• Electric charge is inherently quantized such that the charge on any object is an integer multiple of the smallest unit of charge which is the magnitude of the electron charge
• e = 1.602 × 10 -19^ C.
• On the macroscopic level, we can assume that charge is “continuous.”

Coulomb’s law

• SI standard quantity of a charge is a Coulomb (C) - 1 C = 6.0 x 10 28 electrons - 1.9 x 10 -19^ C = 1 electron (-) or - 1 Proton (+) or 1 “elementary” charge
• Electric Force : (one of the 4 major forces) varies inversely with the distance between the charge - F α 1 d 2

Coulomb’s Law

• Coulomb’s law is the “law of action” between charged bodies.
• Coulomb’s law gives the electric force between two point charges in an otherwise empty universe.
• A point charge is a charge that occupies a region of space which is negligibly small compared to the distance between the point charge and any other object.

 Coulomb’s law

 Like charges repel, unlike charges attract. for the magnitude of the electrostatic force between point charges

 SI unit : Newton, [N]

1 2 2

q q F k r

=

k = 8.99 × 10 9 N m ⋅^2 / C^2

Coulomb’s Law

Coulomb’s Law

2 0 12

1 2 12 4

ˆ (^12) r

Q Q F aR π ε

=

Q (^1)

r 12 Q 2

F 12

Force due to Q (^1) acting on Q 2

Unit vector in direction of R 12

Coulomb’s Law

• The force on Q 1 due to Q 2 is equal in magnitude but opposite in direction to the force on Q 2 due to Q 1.

F 21 = − F 12

 Superposition The electric force on one charge due to two or more other charges is the vector sum of each individual force

 Spherical charge distributions A spherical distribution of charge, when viewed from outside, behaves the same as an equivalent charge at the center of the sphere.

Coulomb’s Law

Coulombs Law: EXAMPLE

• A positive charge of 6.0 x 10 -6^ C is 0.030m from a second positive charge of 3.0 x 10 -6^ C. Calculate the force between the charges.
• Fe = k q 1 q (^2) r 2 = (8.99 x 10 9 N m 2 /C^2 ) (6.0 x 10 -6C) (3.0 x 10 -6C) ( 0.030m ) 2 = (8.99 x 10 9 N m 2 /C^2 ) (18.0 x 10 -12C) (9.0 x 10 -4^ m^2 ) = + 1.8 x 10 -8^ N

Coulombs Law: Summary

• The force of electrical charge is an inverse square of the distance between the charge: - Fe = k q 1 q (^2) r 2

The field strength at any point in this field is:

E = field strength (Vm -1) V = potential difference (V) d = plate separation (m)

d

V

E =

Electric Fields

The Electric Field is defined as the

Force exerted on a tiny positive test

charge at that point divided by the

magnitude of the test charge:

E = Fe q

E is the electric field strength F (^) e is the electrostatic force q is the charge in coulombs

 Definition: The electric field E that exists at a point is the electrostatic force F experienced by a small test charge q0 placed at that point divided by the charge itself.

 Direction of electric field

- A positive charge experiences a force in the direction of E - A negative charge experiences a force in the opposite direction of E (SI unit: N/C)

Electric Field

0

E q

= F

 Magnitude of the electric charge due to a point charge

 Direction:

If the charge q is positive, the field points radically outward

If the charge q is negative, the field points radically inward

Electric Field

r^2

q E = k