Displacement Current - Magnetic Field Through Surface with both Displacement and Conduction Current

  • Recap of Ampere’s law and magnetic field created by conduction current
  • Introduction to displacement current as a concept proposed by Maxwell
  • Definition of displacement current, denoted by I_d
  • Equation for displacement current: I_d = ε0 dϕE/dt, where ε0 is the permittivity of free space, ϕE is the electric flux
  • Comparison of displacement current with conduction current
  • Explanation of how the sum of the two currents contributes to the total magnetic field through a surface
  • Example: Calculation of magnetic field using both conduction and displacement currents
  • Significance of displacement current in understanding electromagnetic waves
  • Applications of displacement current in various fields of physics
  • Summary of key points covered in the lecture

Displacement Current - Magnetic Field Through Surface with both Displacement and Conduction Current

  • Recap of Ampere’s law and magnetic field created by conduction current
  • Introduction to displacement current as a concept proposed by Maxwell
  • Definition of displacement current, denoted by I_d
  • Equation for displacement current: I_d = ε0 dϕE/dt, where ε0 is the permittivity of free space, ϕE is the electric flux
  • Comparison of displacement current with conduction current

Slide 12

  • Explanation of how the sum of the two currents contributes to the total magnetic field through a surface
  • Example: Calculation of magnetic field using both conduction and displacement currents
  • Significance of displacement current in understanding electromagnetic waves
  • Applications of displacement current in various fields of physics
  • Summary of key points covered in the lecture

Ampere’s Law and Magnetic Field

  • Recap of Ampere’s law: ∮B·dl = μ0 × (I_enc + I_dis)
  • Explanation of each term in the equation: B is the magnetic field, dl is the differential length element on a closed loop, I_enc is the conduction current enclosed by the loop, I_dis is the displacement current
  • Magnetic field created by conduction current: B_conduction = μ0 × I_enc / (2πr)
  • Magnetic field created by displacement current: B_displacement = μ0 × I_dis / (2πr)

Displacement Current Concept

  • Introduction to the concept of displacement current proposed by Maxwell
  • Based on the observation that changing electric fields can produce magnetic fields
  • Displacement current accounts for the changing electric fields in Ampere’s law

Definition of Displacement Current

  • Displacement current is a conceptual current that represents the rate of change of electric flux
  • Denoted by I_d
  • Defined as I_d = ε0 dϕE/dt, where ε0 is the permittivity of free space and dϕE/dt is the rate of change of electric flux

Comparison of Displacement and Conduction Current

  • Conduction current is the flow of charges in a conductor due to a potential difference
  • Displacement current is the flow of changing electric fields that contribute to the total magnetic field
  • Conduction current is proportional to the drift velocity of charge carriers, while displacement current is related to the rate of change of electric flux
  • Both conduction and displacement currents contribute to the total magnetic field through a surface

Magnetic Field Calculation with Displacement and Conduction Currents

  • When both conduction and displacement currents exist, the total magnetic field through a surface can be calculated by adding the contributions from both currents: B_total = B_conduction + B_displacement
  • Example: Calculation of magnetic field around a wire carrying both conduction and displacement currents

Significance of Displacement Current

  • Displacement current plays a crucial role in the understanding of electromagnetic waves
  • It explains how changing electric fields can produce varying magnetic fields and vice versa
  • Displacement current allows for the propagation of electromagnetic waves through space

Applications of Displacement Current

  • Displacement current is essential in various fields of physics and engineering
  • It is utilized in the design and operation of antennas and wireless communication systems
  • Displacement current is also significant in the study of electromagnetic induction and the functioning of capacitors

Summary

  • Displacement current is a concept proposed by Maxwell to account for the contribution of changing electric fields in Ampere’s law
  • It is denoted by I_d and is defined as I_d = ε0 dϕE/dt
  • Displacement current adds to the total magnetic field through a surface, along with conduction current
  • It plays a crucial role in understanding electromagnetic waves and finds applications in various fields of physics and engineering

Displacement Current - Magnetic Field Through Surface with both Displacement and Conduction Current

  • Recap of Ampere’s law and magnetic field created by conduction current
  • Introduction to displacement current as a concept proposed by Maxwell
  • Definition of displacement current, denoted by I_d
  • Equation for displacement current: I_d = ε0 dϕE/dt, where ε0 is the permittivity of free space, ϕE is the electric flux
  • Comparison of displacement current with conduction current

Slide 22

  • Explanation of how the sum of the two currents contributes to the total magnetic field through a surface
  • Example: Calculation of magnetic field using both conduction and displacement currents
  • Significance of displacement current in understanding electromagnetic waves
  • Applications of displacement current in various fields of physics
  • Summary of key points covered in the lecture

Ampere’s Law and Magnetic Field

  • Recap of Ampere’s law: ∮B·dl = μ0 × (I_enc + I_dis)
  • Explanation of each term in the equation: B is the magnetic field, dl is the differential length element on a closed loop, I_enc is the conduction current enclosed by the loop, I_dis is the displacement current
  • Magnetic field created by conduction current: B_conduction = μ0 × I_enc / (2πr)
  • Magnetic field created by displacement current: B_displacement = μ0 × I_dis / (2πr)

Displacement Current Concept

  • Introduction to the concept of displacement current proposed by Maxwell
  • Based on the observation that changing electric fields can produce magnetic fields
  • Displacement current accounts for the changing electric fields in Ampere’s law

Definition of Displacement Current

  • Displacement current is a conceptual current that represents the rate of change of electric flux
  • Denoted by I_d
  • Defined as I_d = ε0 dϕE/dt, where ε0 is the permittivity of free space and dϕE/dt is the rate of change of electric flux

Comparison of Displacement and Conduction Current

  • Conduction current is the flow of charges in a conductor due to a potential difference
  • Displacement current is the flow of changing electric fields that contribute to the total magnetic field
  • Conduction current is proportional to the drift velocity of charge carriers, while displacement current is related to the rate of change of electric flux
  • Both conduction and displacement currents contribute to the total magnetic field through a surface

Magnetic Field Calculation with Displacement and Conduction Currents

  • When both conduction and displacement currents exist, the total magnetic field through a surface can be calculated by adding the contributions from both currents: B_total = B_conduction + B_displacement
  • Example: Calculation of magnetic field around a wire carrying both conduction and displacement currents

Significance of Displacement Current

  • Displacement current plays a crucial role in the understanding of electromagnetic waves
  • It explains how changing electric fields can produce varying magnetic fields and vice versa
  • Displacement current allows for the propagation of electromagnetic waves through space

Applications of Displacement Current

  • Displacement current is essential in various fields of physics and engineering
  • It is utilized in the design and operation of antennas and wireless communication systems
  • Displacement current is also significant in the study of electromagnetic induction and the functioning of capacitors

Summary

  • Displacement current is a concept proposed by Maxwell to account for the contribution of changing electric fields in Ampere’s law
  • It is denoted by I_d and is defined as I_d = ε0 dϕE/dt
  • Displacement current adds to the total magnetic field through a surface, along with conduction current
  • It plays a crucial role in understanding electromagnetic waves and finds applications in various fields of physics and engineering