31 October 2019

COULOMB’S LAW

O. M. Oshakuade

Department of Physics,University of Ibadan, Ibadan,

Nigeria.

PHY 104 Lecture Note

Last lecture: Charge and Charge Interactions

Credit: (Young and Freedman, 2012)

Introduction

From the previous lecture, we discussed, like charges repel while unlike charges attract, with forces described by Coulomb’s law.

Coulomb’s law states that the electrical force exerted by one chargedbody on another is directly proportional to the product of themagnitude of the two charges and inversely proportional to the squareof the distance between them.

For two charges of magnitude Q1 and Q2 separated by a distance, r, theforce of interaction, F, between them according to Coulomb’s law ismathematically expressed as:

𝐹 ∝𝑄1 𝑄2

𝑟2

Coulomb’s law

𝐹 ∝𝑄1 𝑄2

𝑟2

𝐹 = 𝑘𝑄1 𝑄2

𝑟2

k is constant of proportionality (Coulomb’s law),

defined as: 𝑘 =1

4𝜋𝜀0≈ 9 × 109 𝑁𝑚2𝐶−2

𝜀0 is permittivity of free space – 8.85 × 10−12 𝑁−1𝑚−2𝐶2

𝐹 =𝑄1 𝑄2

4𝜋𝜀0𝑟2

Coulomb’s Force

(i) Obeys the superposition principle. That is 𝐹 = 𝐹𝑛,

where n = 1, 2, 3, …, n-1,

(ii) It is a conservative force; a conservative force is a force with the

property that the work done in moving a particle between two points is

independent of the path taken., and

(iii) It is a central force. That is, it acts along the line joining the two point

charges.

Coulomb’s Force

EXAMPLE: The electron and proton of a hydrogen atom are separated (on the average) by a distance of approximately 5.3 × 10−11𝑚. Find the magnitude of the electric force between the two particles.

Coulomb’s Force

Force is a vector quantity, this is important when applying Coulomb’s law.Coulomb’s law expressed in vector form for the electric force exerted by a

charge 𝑞1 on a second charge 𝑞2, is 𝐹12 =𝑞1𝑞2

4𝜋𝜀0𝑟2 𝑟12

Where 𝑟12 is a unit vector directed from 𝑞1 toward 𝑞2 as shown below.

Because the electric force obeys Newton’s third law, the electric force exerted by 𝑞2 on 𝑞1 is equal in magnitude to the force exerted by 𝑞1 on 𝑞2 and in the opposite direction.

Electric Force

Example: Consider three point charges located at the corners of a right triangle as shown below, where q1 = q3 = 5.0 μC, q2 = - 2.0 μC, and a =0.10 m. Find the resultant force exerted on q3.

Electric Force

Electric Force

Electric Force

Electric ForceOO1

4 November 2018

ELECTRIC FIELD

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