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Chapter 2 
 
Coulomb’s Law 
 
2.1 Electric Charge.....................................................................................................2-3 
2.2 Coulomb's Law ....................................................................................................2-3 
Animation 2.1: Van de Graaff Generator...............................................................2-4 
2.3 Principle of Superposition....................................................................................2-5 
Example 2.1: Three Charges....................................................................................2-5 
2.4 Electric Field........................................................................................................2-7 
Animation 2.2: Electric Field of Point Charges .....................................................2-8 
2.5 Electric Field Lines..............................................................................................2-9 
2.6 Force on a Charged Particle in an Electric Field ...............................................2-10 
2.7 Electric Dipole ...................................................................................................2-11 
2.7.1 The Electric Field of a Dipole......................................................................2-12 
Animation 2.3: Electric Dipole.............................................................................2-13 
2.8 Dipole in Electric Field......................................................................................2-13 
2.8.1 Potential Energy of an Electric Dipole ........................................................2-14 
2.9 Charge Density...................................................................................................2-16 
2.9.1 Volume Charge Density...............................................................................2-16 
2.9.2 Surface Charge Density ...............................................................................2-17 
2.9.3 Line Charge Density ....................................................................................2-17 
2.10 Electric Fields due to Continuous Charge Distributions....................................2-18 
Example 2.2: Electric Field on the Axis of a Rod .................................................2-18 
Example 2.3: Electric Field on the Perpendicular Bisector ...................................2-19 
Example 2.4: Electric Field on the Axis of a Ring ................................................2-21 
Example 2.5: Electric Field Due to a Uniformly Charged Disk............................2-23 
2.11 Summary............................................................................................................2-25 
2.12 Problem-Solving Strategies ...............................................................................2-27 
2.13 Solved Problems ................................................................................................2-29 
2.13.1 Hydrogen Atom ........................................................................................2-29 
2.13.2 Millikan Oil-Drop Experiment .................................................................2-30 
2.13.3 Charge Moving Perpendicularly to an Electric Field ...............................2-31 
2.13.4 Electric Field of a Dipole..........................................................................2-33 
 2-1
Page 2


 
 
Chapter 2 
 
Coulomb’s Law 
 
2.1 Electric Charge.....................................................................................................2-3 
2.2 Coulomb's Law ....................................................................................................2-3 
Animation 2.1: Van de Graaff Generator...............................................................2-4 
2.3 Principle of Superposition....................................................................................2-5 
Example 2.1: Three Charges....................................................................................2-5 
2.4 Electric Field........................................................................................................2-7 
Animation 2.2: Electric Field of Point Charges .....................................................2-8 
2.5 Electric Field Lines..............................................................................................2-9 
2.6 Force on a Charged Particle in an Electric Field ...............................................2-10 
2.7 Electric Dipole ...................................................................................................2-11 
2.7.1 The Electric Field of a Dipole......................................................................2-12 
Animation 2.3: Electric Dipole.............................................................................2-13 
2.8 Dipole in Electric Field......................................................................................2-13 
2.8.1 Potential Energy of an Electric Dipole ........................................................2-14 
2.9 Charge Density...................................................................................................2-16 
2.9.1 Volume Charge Density...............................................................................2-16 
2.9.2 Surface Charge Density ...............................................................................2-17 
2.9.3 Line Charge Density ....................................................................................2-17 
2.10 Electric Fields due to Continuous Charge Distributions....................................2-18 
Example 2.2: Electric Field on the Axis of a Rod .................................................2-18 
Example 2.3: Electric Field on the Perpendicular Bisector ...................................2-19 
Example 2.4: Electric Field on the Axis of a Ring ................................................2-21 
Example 2.5: Electric Field Due to a Uniformly Charged Disk............................2-23 
2.11 Summary............................................................................................................2-25 
2.12 Problem-Solving Strategies ...............................................................................2-27 
2.13 Solved Problems ................................................................................................2-29 
2.13.1 Hydrogen Atom ........................................................................................2-29 
2.13.2 Millikan Oil-Drop Experiment .................................................................2-30 
2.13.3 Charge Moving Perpendicularly to an Electric Field ...............................2-31 
2.13.4 Electric Field of a Dipole..........................................................................2-33 
 2-1
2.13.5 Electric Field of an Arc.............................................................................2-36 
2.13.6 Electric Field Off the Axis of a Finite Rod...............................................2-37 
2.14 Conceptual Questions ........................................................................................2-39 
2.15 Additional Problems ..........................................................................................2-40 
2.15.1 Three Point Charges..................................................................................2-40 
2.15.2 Three Point Charges..................................................................................2-40 
2.15.3 Four Point Charges ...................................................................................2-41 
2.15.4 Semicircular Wire .....................................................................................2-41 
2.15.5 Electric Dipole ..........................................................................................2-42 
2.15.6 Charged Cylindrical Shell and Cylinder...................................................2-42 
2.15.7 Two Conducting Balls ..............................................................................2-43 
2.15.8 Torque on an Electric Dipole....................................................................2-43 
 
 
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FAQs on Electric Field Charge Notes - Physics for Grade 12

1. What is an electric field?
Ans. An electric field is a region surrounding a charged object or group of objects within which a force would be exerted on other charged objects. It is created by the presence of electric charges and can be either positive or negative.
2. How is the electric field calculated?
Ans. The electric field at a specific point can be calculated by dividing the force exerted on a test charge by the magnitude of the test charge. Mathematically, it is represented as E = F/q, where E is the electric field, F is the force, and q is the test charge.
3. What is the relationship between electric field and charge?
Ans. The electric field is directly proportional to the charge that created it. This means that an increase in the charge will result in a stronger electric field, while a decrease in the charge will result in a weaker electric field.
4. How does the direction of the electric field depend on the charge?
Ans. The direction of the electric field depends on the type of charge. For a positive charge, the electric field lines radiate outward, away from the charge. For a negative charge, the electric field lines converge inward, towards the charge.
5. What are some real-life applications of electric fields?
Ans. Electric fields have various real-life applications. Some examples include the operation of electronic devices, such as televisions and computers, the functioning of electric motors, and the generation and transmission of electricity in power grids. Electric fields are also used in medical procedures like electrocardiograms (ECGs) and electroencephalograms (EEGs).
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