a. ELECTROMAGNETIC WAVES WAX
James Clerk Maxwell proposed that just like a magnetic field changing with time produces an electric field, a time
varying electric field also produces a magnetic field.
Maxwell formulated a set of equations involving electric and magnetic field. The Maxwell equations along with
Lorentz force formula mathematically express all the basic laws of Electromagnetism
Unification of Electricity, Magnetism and Light
Maxwell’s equation predicted the existence of electromagnetic waves. The speed of the wave according to these
equations came out to be very close to the speed of light (c= 3 × 108 m/s) obtained by measurements. This led to the
conclusion that light is an electromagnetic wave.
Mx Displacement current (PYQ 2018, 2016)
The current produced due to changing electric field (electric displacement) is called displacement current.
Consider a capacitor C. Let us observe the process of charging the capacitor and apply Ampere’s Circuital Law –
To find the field at a point P just outside the capacitor, consider a plane circular loop of radius r with its plane
perpendicular to the direction of the current carrying wire. From symmetry we can say that the field is directed
along the circumference of the loop and is of the same magnitude at all points. Therefore-
Now consider another surface with the same boundary and a pot like surface and has its bottom between the plates
of the capacitor (fig i) and another surface like a tiffin box (fig ii) (all three are of the same perimeter). Applying ACL
to them, we find that the left side of the equation has not changed but the right side becomes 0 as no current passes
through the surface. Therefore, we conclude a term must be missing from ACL.
to find this missing term, consider the electric field passing between the two plates. Let the charge on the plates be
Q, Area A then the magnitude of field between the BoB fields-
H
µ,
The flux through surface-
Now if there is any current through the surface of the capacitors , it can be written as i= dQ/dt
This is the missing term in Ampere’s circuital law and is called the displacement current (id)
, Note: 1. The total current carried by conductors due to flow of charges is called the conduction current (ic)
2. Thus Maxwell concluded that the source of magnetic field is not just the conduction current but also the rate of
change of electric field w.r.t. time. I.e. the total current is the sum of conduction current and displacement current-
Outside the capacitor there is only conduction current and inside the capacitor, there is only displacement current.
Wx Ampere-Maxwell Law (Modified Ampere’s circuital law) (PYQ 2020, 2016)
The total current passing through any surface of which the closed loop is the perimeter is the sum of the conduction
current and the displacement current.
Note: There are regions where there is no conduction current but only displacement current for e.g. between the
plates of a charging/discharging capacitor
And there are regions where there is only conduction current and no displacement current for e.g. a wire carrying
steady current or outside a capacitor. (PYQ 2018)
Wx Maxwell’s Equations
The following ••
five equations are called Maxwell’s equations-
four
1)
2)
3)
4)
Important PYQs ties
Ques: Write the mathematical form of Ampere- Maxwell law (PYQ 2020) [1M]
Ans:
Ques: Give one example each to illustrate where there is i) displacement current but no conduction current ii) only
conduction current but no displacement current (PYQ 2018) [1M]
Ans: i) Between the plates of a charging/discharging capacitor
ii) outside the capacitor plates
Ques: Write Maxwell’s generalization of ACL. Show that in charging a capacitor, the current produced within the
plates of a capacitor is -
James Clerk Maxwell proposed that just like a magnetic field changing with time produces an electric field, a time
varying electric field also produces a magnetic field.
Maxwell formulated a set of equations involving electric and magnetic field. The Maxwell equations along with
Lorentz force formula mathematically express all the basic laws of Electromagnetism
Unification of Electricity, Magnetism and Light
Maxwell’s equation predicted the existence of electromagnetic waves. The speed of the wave according to these
equations came out to be very close to the speed of light (c= 3 × 108 m/s) obtained by measurements. This led to the
conclusion that light is an electromagnetic wave.
Mx Displacement current (PYQ 2018, 2016)
The current produced due to changing electric field (electric displacement) is called displacement current.
Consider a capacitor C. Let us observe the process of charging the capacitor and apply Ampere’s Circuital Law –
To find the field at a point P just outside the capacitor, consider a plane circular loop of radius r with its plane
perpendicular to the direction of the current carrying wire. From symmetry we can say that the field is directed
along the circumference of the loop and is of the same magnitude at all points. Therefore-
Now consider another surface with the same boundary and a pot like surface and has its bottom between the plates
of the capacitor (fig i) and another surface like a tiffin box (fig ii) (all three are of the same perimeter). Applying ACL
to them, we find that the left side of the equation has not changed but the right side becomes 0 as no current passes
through the surface. Therefore, we conclude a term must be missing from ACL.
to find this missing term, consider the electric field passing between the two plates. Let the charge on the plates be
Q, Area A then the magnitude of field between the BoB fields-
H
µ,
The flux through surface-
Now if there is any current through the surface of the capacitors , it can be written as i= dQ/dt
This is the missing term in Ampere’s circuital law and is called the displacement current (id)
, Note: 1. The total current carried by conductors due to flow of charges is called the conduction current (ic)
2. Thus Maxwell concluded that the source of magnetic field is not just the conduction current but also the rate of
change of electric field w.r.t. time. I.e. the total current is the sum of conduction current and displacement current-
Outside the capacitor there is only conduction current and inside the capacitor, there is only displacement current.
Wx Ampere-Maxwell Law (Modified Ampere’s circuital law) (PYQ 2020, 2016)
The total current passing through any surface of which the closed loop is the perimeter is the sum of the conduction
current and the displacement current.
Note: There are regions where there is no conduction current but only displacement current for e.g. between the
plates of a charging/discharging capacitor
And there are regions where there is only conduction current and no displacement current for e.g. a wire carrying
steady current or outside a capacitor. (PYQ 2018)
Wx Maxwell’s Equations
The following ••
five equations are called Maxwell’s equations-
four
1)
2)
3)
4)
Important PYQs ties
Ques: Write the mathematical form of Ampere- Maxwell law (PYQ 2020) [1M]
Ans:
Ques: Give one example each to illustrate where there is i) displacement current but no conduction current ii) only
conduction current but no displacement current (PYQ 2018) [1M]
Ans: i) Between the plates of a charging/discharging capacitor
ii) outside the capacitor plates
Ques: Write Maxwell’s generalization of ACL. Show that in charging a capacitor, the current produced within the
plates of a capacitor is -
