Ampere Maxwell's equation

Ampere-Maxwell’s Law: Maxwell correction to Ampere’s Law
Maxwell said that there has to be some current existing between plates. There are no conduction electrons between plates BUT there is time-varying E between plates, which generates a current. The E is directed from +ve plate to –ve plate, because the amount of charge on capacitor increases with time, AND
The E between plates increases with time, as well. He called this new current as a displacement current.
Here are links of other videos on Maxwell's equations:

Electric Field due to a Solid Sphere of Charge (Gauss’s Law for Electrostatics: Applications)
https://www.youtube.com/watch?v=sp5qV
Electric Field due to Uniform Spherical Shell of Charge
https://www.youtube.com/watch?v=AnPvK...
Ampere's law:
https://www.youtube.com/watch?v=y-DpDn6BI_Q


Applications of Gauss's law: Electric field due to an infinitely large plane sheet of charge:
https://www.youtube.com/watch?v=oJ7bA...

Applications of Gauss’s law: Electric field of an infinitely long uniformly charged conductor
https://www.youtube.com/watch?v=FwssH...

1. 4. Ampere-Maxwell’s Law Ampere’s Law ‘ The line integral of the magnetic field B around any closed loop is times the net steady current I enclosed by this path ”   Maxwell’s Equations (1) dl I p B B . dl = B dl cos 0= B dl As, B is uniform at each point on the field line: B . dl = B (2 π r) (2) Equating (1) and (2): B =   i.e. the magnetic field a distance r from a long straight wire carrying a steady current I. https://www.youtube.com/channel/UC1hrAjhSKGAsWZ7LvR_rbRg Here is a link of Youtube video. You can watch this lecture on Youtube , as well.

2. 4. Ampere-Maxwell’s Law Ampere’s Law ‘ The line integral of the magnetic field B around any closed loop is times the net steady current I enclosed by this path ”   Maxwell’s Equations (1) dl I p B B . dl = B dl cos 0= B dl As, B is uniform at each point on the field line: B . dl = B (2 π r) (2) Equating (1) and (2): B =   i.e. the magnetic field a distance r from a long straight wire carrying a steady current I. Ampere’s law is true for steady currents T he Magnetic field inside the loop remains constant I , arising due to flow of charges, is called the ’ conduction current’ I C c

3. 4. Ampere and Maxwell’s Law Ampere’s Law ‘ The line integral of the magnetic field B around any closed loop is times the net steady current I enclosed by this path ”   Maxwell’s Equations (1) dl I p B B . dl = B dl cos 0= B dl As, B is uniform at each point on the field line: B . dl = B (2 π r) (2) Equating (1) and (2): B =   i.e. the magnetic field a distance r from a long straight wire carrying a steady current I. Ampere’s law is true for steady currents T he Magnetic field inside the loop remains constant I , arising due to flow of charges, is called the ’ conduction current’ I C c Let’s there is a capacitor and the Amperian surface is like a bag and its top is open : L A Ampere’s Law

4. 4. Ampere and Maxwell’s Law Ampere’s Law ‘ The line integral of the magnetic field B around any closed loop is times the net steady current I enclosed by this path ”   Maxwell’s Equations (1) dl I p B B . dl = B dl cos 0= B dl As, B is uniform at each point on the field line: B . dl = B (2 π r) (2) Equating (1) and (2): B =   i.e. the magnetic field a distance r from a long straight wire carrying a steady current I. Ampere’s law is true for steady currents T he Magnetic field inside the loop remains constant I , arising due to flow of charges, is called the ’ conduction current’ I C c Let’s there is a capacitor and the Amperian surface is like a bag and its top is open : + + + + + - - - - - - - - - - + + + + + L A Ampere’s Law

5. 4. Ampere and Maxwell’s Law Ampere’s Law ‘ The line integral of the magnetic field B around any closed loop is times the net steady current I enclosed by this path ”   Maxwell’s Equations (1) dl I p B B . dl = B dl cos 0= B dl As, B is uniform at each point on the field line: B . dl = B (2 π r) (2) Equating (1) and (2): B =   i.e. the magnetic field a distance r from a long straight wire carrying a steady current I. Ampere’s law is true for steady currents T he Magnetic field inside the loop remains constant I , arising due to flow of charges, is called the ’ conduction current’ I C c Let’s there is a capacitor and the Amperian surface is like a bag and its top is open : + + + + + - - - - - - - - - - + + + + + L A Ampere’s Law

6. 4. Ampere and Maxwell’s Law Ampere’s Law ‘ The line integral of the magnetic field B around any closed loop is times the net steady current I enclosed by this path ”   Maxwell’s Equations (1) dl I p B B . dl = B dl cos 0= B dl As, B is uniform at each point on the field line: B . dl = B (2 π r) (2) Equating (1) and (2): B =   i.e. the magnetic field a distance r from a long straight wire carrying a steady current I. Ampere’s law is true for steady currents T he Magnetic field inside the loop remains constant I , arising due to flow of charges, is called the ’ conduction current’ I C c Let’s there is a capacitor and the Amperian surface is like a bag and its top is open : + + + + + - - - - - - - - - - + + + + + As there is no current flowing inside the capacitor, hence B . dl = 0. At the same point ‘P’ but with different A mperian surfaces, the B is not same. Conc : There are some gaps in the Ampere’s law. Maxwell corrected and made Ampere’s law consistent in all cases . What happens between the plates while the current  I  is flowing? L A Ampere’s Law

7. Maxwell’s Equations + + + + + - - - - - - - - - - + + + + + E Maxwell correction to Ampere’s Law There has to be some I existing between plates. There are no conduction electrons between plates BUT There is time-varying E between plates, which generates I . The E is directed from + ve plate to – ve plate, because the amount of charge on capacitor increases with time, AND The E between plates increases with time, as well. He called this new current as a displacement current, I d   .

8. Maxwell’s Equations As the amount of charge on the capacitor increases with time, hence the q charge, changes with time, produces a current: I d    = dq /dt + + + + + - - - - - - - - - - + + + + + E For a capacitor, , and Maxwell correction to Ampere’s Law There has to be some I existing between plates. There are no conduction electrons between plates BUT There is time-varying E between plates, which generates I . The E is directed from + ve plate to – ve plate, because the amount of charge on capacitor increases with time, AND The E between plates increases with time, as well. He called this new current as a displacement current, I d   . Φ E d i.e. Current is produced because of changing electric flux w.r.t time OR Electric flux is generated due to the presence of E between plates.

9. Maxwell’s Equations As the amount of charge on the capacitor increases with time, hence the q charge, changes with time, produces a current: I d    = dq /dt + + + + + - - - - - - - - - - + + + + + E For a capacitor, , and Maxwell correction to Ampere’s Law There has to be some I existing between plates. There are no conduction electrons between plates BUT There is time-varying E between plates, which generates I . The E is directed from + ve plate to – ve plate, because the amount of charge on capacitor increases with time, AND The E between plates increases with time, as well. He called this new current as a displacement current, I d   . Φ E d i.e. Current is produced because of changing electric flux w.r.t time OR Electric flux is generated due to the presence of E between plates. CONC: Cur rent is not ZERO between plates but it is I d   AND B is produced by the time varying E or I d  

10. Maxwell’s Equations As the amount of charge on the capacitor increases with time, hence the q charge, changes with time, produces a current: I d    = dq /dt + + + + + - - - - - - - - - - + + + + + E For a capacitor, , and Maxwell correction to Ampere’s Law There has to be some I existing between plates. There are no conduction electrons between plates BUT There is time-varying E between plates, which generates I . The E is directed from + ve plate to – ve plate, because the amount of charge on capacitor increases with time, AND The E between plates increases with time, as well. He called this new current as a displacement current, I d   . Φ E d Conc : B s are produced both by a conduction current and by a time-varying field. A changing electric field induces a magnetic field Maxwell correction to Ampere’s Law is: c c i.e. Current is produced because of changing electric flux w.r.t time OR Electric flux is generated due to the presence of E between plates CONC: Cur rent is not ZERO between plates but it is I d   AND B is produced by the time varying E or I d  

11. Maxwell’s Equations As the amount of charge on the capacitor increases with time, hence the q charge, changes with time, produces a current: I d    = dq /dt + + + + + - - - - - - - - - - + + + + + E For a capacitor, , and Maxwell correction to Ampere’s Law There has to be some I existing between plates. There are no conduction electrons between plates BUT There is time-varying E between plates, which generates I . The E is directed from + ve plate to – ve plate, because the amount of charge on capacitor increases with time, AND The E between plates increases with time, as well. He called this new current as a displacement current, I d   . Φ E d Conc : B s are produced both by a conduction current and by a time-varying field. A changing electric field induces a magnetic field Maxwell correction to Ampere’s Law is: c c i.e. Current is produced because of changing electric flux w.r.t time OR Electric flux is generated due to the presence of E between plates CONC: Cur rent is not ZERO between plates but it is I d   AND B is produced by the time varying E or I d