Concept of charge and Coulomb’s law - Properties of Charges

  • Electric Charge
  • Types of Charges
  • Conservation of Charge
  • Coulomb’s Law
  • Principle of Superposition

Electric Charge

  • Fundamental property of matter
  • Two types: Positive (+) and Negative (-)
  • Like charges repel, unlike charges attract
  • Charge is quantized (integer multiples of the elementary charge)

Types of Charges

  • Protons: Positive charge (+)
  • Electrons: Negative charge (-)
  • Neutrons: No charge (neutral)

Conservation of Charge

  • Total charge in a closed system remains constant
  • The net charge before and after an interaction is the same
  • Charge is neither created nor destroyed, only transferred or redistributed

Coulomb’s Law

  • Describes the force between two point charges
  • The force is directly proportional to the product of the charges
  • The force is inversely proportional to the square of the distance between the charges
  • Mathematically represented as: F = k * (q1 * q2) / r^2

Principle of Superposition

  • Total force on a charge due to multiple charges is the vector sum of the forces due to individual charges
  • The principle applies to both attractive and repulsive forces
  • The resulting force can be calculated by considering each pair of charges separately and then summing the vector forces

Examples

Example 1:

  • Two charges of +5C and -3C are placed 2m apart. Calculate the force between them.
  • Solution: F = k * (q1 * q2) / r^2
  • Substitute the values: F = (9 * 10^9 N m^2/C^2) * ((5C) * (-3C)) / (2m)^2
  • Calculate the force using the equation.

Examples (contd.)

Example 2:

  • Three charges of +2C, -4C, and +6C are placed in a line. Find the net force on the +2C charge.
  • Solution: Use the principle of superposition to calculate the force between the +2C charge and each of the other charges.
  • Add the vector forces to find the total force on the +2C charge.

Equations

  • Coulomb’s Law: F = k * (q1 * q2) / r^2
  • Principle of Superposition: F_tot = F1 + F2 + F3 + … + Fn
  • k is the electrostatic constant (9 * 10^9 N m^2/C^2) Note: Ensure proper units are used while calculating and representing the equations.

Electric Fields

  • Electric Field concept
  • Electric Field due to a single charge
  • Electric Field due to multiple charges
  • Electric Field Lines
  • Electric Field Strength

Electric Field Concept

  • Electric field created by a charge in its surrounding space
  • Measured in N/C (Newton per Coulomb)
  • Represents the force experienced by a positive test charge placed in the field

Electric Field due to a Single Charge

  • Electric field lines radiate outwards from a positive charge
  • Electric field lines terminate on a negative charge
  • The strength of the electric field decreases with distance from the charge
  • Mathematically represented as: E = k * (Q / r^2)

Electric Field due to Multiple Charges

  • Superposition principle applies to electric fields
  • The total electric field at a point is the vector sum of the individual electric fields
  • Calculate the electric field contributions from each charge and add them vectorially

Electric Field Lines

  • Imaginary lines that represent the direction and strength of an electric field
  • Direction: Shows the direction a positive test charge would move if placed in the field
  • Density: Closer lines indicate a stronger electric field
  • Electric field lines never intersect

Electric Field Strength

  • The measure of the force experienced by a positive test charge placed in the electric field
  • The electric field strength is directly proportional to the force experienced by the charge
  • Mathematically represented as: E = F / q

Examples

Example 1:

  • A +3C charge creates an electric field of 200 N/C at a certain point. What is the force experienced by a +2C test charge placed at that point?
  • Solution: Use the equation E = F / q and rearrange it to calculate the force. Example 2:
  • Two charges of +4C and -2C create electric fields of 80 N/C and 120 N/C respectively at a certain point. Find the electric field at that point due to both charges.
  • Solution: Calculate the electric field contributions from each charge using the equation E = k * (Q / r^2) and add them vectorially.

Equations

  • Electric Field due to a single charge: E = k * (Q / r^2)
  • Electric Field Strength: E = F / q Note: Make sure to use the appropriate units while substituting the values in the equations.

Summary

  • Electric fields are created by charges in their surrounding space
  • Electric field lines represent the direction and strength of the electric field
  • The electric field can be calculated using Coulomb’s law and the principle of superposition
  • Electric field strength is directly proportional to the force experienced by a test charge
  • Proper units and vector sum must be considered when working with electric fields

Review Questions

  1. Define electric field and explain its significance.
  1. How does the electric field due to a positive charge differ from that due to a negative charge?
  1. What is the superposition principle in relation to electric fields?
  1. How can electric field lines be used to visualize an electric field?
  1. State the formula for calculating electric field strength. Note: These review questions can help reinforce the concepts covered in this lecture.
  1. Electric Potential Energy
  • Definition of electric potential energy
  • Formula for electric potential energy
  • Work done in moving a charge
  • Relationship between electric potential energy and work done
  1. Definition of Electric Potential Energy
  • Potential energy associated with a charged particle in an electric field
  • Depends on the position and charge of the particle
  • Measured in joules (J)
  1. Formula for Electric Potential Energy
  • Electric potential energy (PE) = q * V
  • q is the charge of the particle
  • V is the electric potential at the position of the particle
  1. Work Done in Moving a Charge
  • Work done (W) = change in electric potential energy
  • ΔPE = q * (ΔV)
  • q is the charge of the particle
  • ΔV is the change in electric potential
  1. Relationship Between Electric Potential Energy and Work Done
  • Work done to move a charge against the electric field increases its electric potential energy
  • Work done by the electric field in moving the charge reduces its electric potential energy
  • Work done is negative when the charge is moved in the direction of the field
  • Work done is positive when the charge is moved opposite to the field
  1. Examples Example 1:
  • A +4C charge is moved from a point with a potential of 200V to another point with a potential of 150V. Calculate the change in electric potential energy.
  • Solution: ΔPE = q * (ΔV)
  • Substitute the values: ΔPE = (4C) * (150V - 200V)
  • Calculate the change in electric potential energy.
  1. Examples (contd.) Example 2:
  • A charge of -10μC is released from rest and moves towards a positive charge. The final electric potential energy is -40μJ. Calculate the work done by the electric field.
  • Solution: Work done (W) = ΔPE
  • Substitute the values: W = -40μJ
  • Calculate the work done by the electric field.
  1. Equations
  • Electric Potential Energy: PE = q * V
  • Work Done: W = ΔPE = q * ΔV Note: Ensure proper units are used while calculating and representing the equations.
  1. Summary
  • Electric potential energy depends on the position and charge of a particle in an electric field
  • The work done in moving a charge is equal to the change in electric potential energy
  • Work done is positive when moving opposite to the field and negative when moving in the field direction
  • Equations provide a framework for calculating electric potential energy and work done
  1. Review Questions
  1. Define electric potential energy and its unit of measurement.
  1. How is work done related to the change in electric potential energy?
  1. Explain the significance of the positive or negative sign of work done in moving a charge.
  1. What is the formula for calculating electric potential energy?
  1. Give an example of calculating the change in electric potential energy for a moving charge. Note: These review questions can help reinforce the concepts covered in this lecture.