Moving Charges & Magnetism Class 12 Notes Physics Chapter 4

 Page 1


 
                                              
Revision Notes 
Physics 
Moving Charges and Magnetism 
 
Electromagnetics: 
? Magnetic effects of electric current is a branch of physics that studies the 
influence of a magnetic field produced by a current or moving charge. 
 
Magnetic Field: 
? It is a region or place where the magnetic effect of a magnet, current 
carrying conductor, or moving charge can be felt. 
?  The tesla is the SI unit for it (T). 
 
Biot-Savart Law: 
? According to this law, " the magnetic flux density of which dB, is directly 
proportional to the length of the element dl, the current I, is given by 
2 0
2
sin
  Wb / m
4
idl
dB
r
? ?
?
? or tesla 
            
 
Page 2


 
                                              
Revision Notes 
Physics 
Moving Charges and Magnetism 
 
Electromagnetics: 
? Magnetic effects of electric current is a branch of physics that studies the 
influence of a magnetic field produced by a current or moving charge. 
 
Magnetic Field: 
? It is a region or place where the magnetic effect of a magnet, current 
carrying conductor, or moving charge can be felt. 
?  The tesla is the SI unit for it (T). 
 
Biot-Savart Law: 
? According to this law, " the magnetic flux density of which dB, is directly 
proportional to the length of the element dl, the current I, is given by 
2 0
2
sin
  Wb / m
4
idl
dB
r
? ?
?
? or tesla 
            
 
 
                                              
? 
0
3
4
id
dB
r
?
?
?
?
r
 
Here, 
0
? is a constant and it is called the permeability of free space and it 
is given as, 
7
0
4 10   Wb / A m ??
?
? ? ? 
 
Applications of Biot-Savart's Law 
? Biot-Savart law is used to calculate magnetic responses even at the atomic 
or molecular level. 
? Biot-Savart law is used in aerodynamic theory to calculate the velocity 
induced by vortex lines. 
 
Importance of Biot-Savart Law 
? Coulomb's law is similar to Biot-Savart law in electrostatics. 
? Biot-Savart law is also applicable for very small conductors carrying 
current. 
? Biot-Savart law is applicable for symmetrical current distribution. 
 
Rules to Find the Direction of Magnetic Field: 
? Right hand palm rule: The direction of the field will be perpendicular to 
the palm if we spread our right hand in such a way that the thumb is facing 
the direction of current and the fingers are facing the spot where we need 
to identify the direction of the field. 
? Maxwell's right handed screw rule: When the tip of a right-handed 
corkscrew moves in the direction of current flow through the conductor, 
the rotation of the screw's head gives the direction of magnetic lines of 
force. 
 
Ampere's Circuital Law: 
Page 3


 
                                              
Revision Notes 
Physics 
Moving Charges and Magnetism 
 
Electromagnetics: 
? Magnetic effects of electric current is a branch of physics that studies the 
influence of a magnetic field produced by a current or moving charge. 
 
Magnetic Field: 
? It is a region or place where the magnetic effect of a magnet, current 
carrying conductor, or moving charge can be felt. 
?  The tesla is the SI unit for it (T). 
 
Biot-Savart Law: 
? According to this law, " the magnetic flux density of which dB, is directly 
proportional to the length of the element dl, the current I, is given by 
2 0
2
sin
  Wb / m
4
idl
dB
r
? ?
?
? or tesla 
            
 
 
                                              
? 
0
3
4
id
dB
r
?
?
?
?
r
 
Here, 
0
? is a constant and it is called the permeability of free space and it 
is given as, 
7
0
4 10   Wb / A m ??
?
? ? ? 
 
Applications of Biot-Savart's Law 
? Biot-Savart law is used to calculate magnetic responses even at the atomic 
or molecular level. 
? Biot-Savart law is used in aerodynamic theory to calculate the velocity 
induced by vortex lines. 
 
Importance of Biot-Savart Law 
? Coulomb's law is similar to Biot-Savart law in electrostatics. 
? Biot-Savart law is also applicable for very small conductors carrying 
current. 
? Biot-Savart law is applicable for symmetrical current distribution. 
 
Rules to Find the Direction of Magnetic Field: 
? Right hand palm rule: The direction of the field will be perpendicular to 
the palm if we spread our right hand in such a way that the thumb is facing 
the direction of current and the fingers are facing the spot where we need 
to identify the direction of the field. 
? Maxwell's right handed screw rule: When the tip of a right-handed 
corkscrew moves in the direction of current flow through the conductor, 
the rotation of the screw's head gives the direction of magnetic lines of 
force. 
 
Ampere's Circuital Law: 
 
                                              
? Ampere's Circuital Law states that the line integral of the magnetic field 
around any closed path in vacuum is equal to 
0
? times the total current 
enclosed by the loop. 
             
0 net 
dI ? ??
?
B1 
? The simplified form of it is 
0 net 
BI ? ? , this equation is used in the following 
conditions. 
o At every point of the closed circuit B dl ? . 
o The magnetic field in the closed circuit is uniform at all points. 
 
Ampere's Law states that the magnetic field generated by an electric current is 
proportional to the size of the electric current. 
Gauss's law states that the electric flux through any closed surface is equal to the 
total charge inside divided by 
0
? . Charges are the source and sinks of the electric 
field. 
Biot-Savart's law states that the magnetic intensity at any point along an 
infinitely long straight wire caused by a constant current is exactly proportional 
to the current and inversely proportional to the distance between point and wire. 
According to this, coulomb's law states that the amount of the electrostatic force 
of attraction between two point charges is directly proportional to the product of 
the charges' magnitudes and inversely proportional to the square of the distance 
between them formula. 
12
2
kq q
F
d
? 
 
Application of Ampere's Circuital Law: 
? The following are the principal applications of Ampere's circuital law: 
? The magnetic field produced by an infinitely long straight wire 
0
2
I
B
r
?
?
?? 
Page 4


 
                                              
Revision Notes 
Physics 
Moving Charges and Magnetism 
 
Electromagnetics: 
? Magnetic effects of electric current is a branch of physics that studies the 
influence of a magnetic field produced by a current or moving charge. 
 
Magnetic Field: 
? It is a region or place where the magnetic effect of a magnet, current 
carrying conductor, or moving charge can be felt. 
?  The tesla is the SI unit for it (T). 
 
Biot-Savart Law: 
? According to this law, " the magnetic flux density of which dB, is directly 
proportional to the length of the element dl, the current I, is given by 
2 0
2
sin
  Wb / m
4
idl
dB
r
? ?
?
? or tesla 
            
 
 
                                              
? 
0
3
4
id
dB
r
?
?
?
?
r
 
Here, 
0
? is a constant and it is called the permeability of free space and it 
is given as, 
7
0
4 10   Wb / A m ??
?
? ? ? 
 
Applications of Biot-Savart's Law 
? Biot-Savart law is used to calculate magnetic responses even at the atomic 
or molecular level. 
? Biot-Savart law is used in aerodynamic theory to calculate the velocity 
induced by vortex lines. 
 
Importance of Biot-Savart Law 
? Coulomb's law is similar to Biot-Savart law in electrostatics. 
? Biot-Savart law is also applicable for very small conductors carrying 
current. 
? Biot-Savart law is applicable for symmetrical current distribution. 
 
Rules to Find the Direction of Magnetic Field: 
? Right hand palm rule: The direction of the field will be perpendicular to 
the palm if we spread our right hand in such a way that the thumb is facing 
the direction of current and the fingers are facing the spot where we need 
to identify the direction of the field. 
? Maxwell's right handed screw rule: When the tip of a right-handed 
corkscrew moves in the direction of current flow through the conductor, 
the rotation of the screw's head gives the direction of magnetic lines of 
force. 
 
Ampere's Circuital Law: 
 
                                              
? Ampere's Circuital Law states that the line integral of the magnetic field 
around any closed path in vacuum is equal to 
0
? times the total current 
enclosed by the loop. 
             
0 net 
dI ? ??
?
B1 
? The simplified form of it is 
0 net 
BI ? ? , this equation is used in the following 
conditions. 
o At every point of the closed circuit B dl ? . 
o The magnetic field in the closed circuit is uniform at all points. 
 
Ampere's Law states that the magnetic field generated by an electric current is 
proportional to the size of the electric current. 
Gauss's law states that the electric flux through any closed surface is equal to the 
total charge inside divided by 
0
? . Charges are the source and sinks of the electric 
field. 
Biot-Savart's law states that the magnetic intensity at any point along an 
infinitely long straight wire caused by a constant current is exactly proportional 
to the current and inversely proportional to the distance between point and wire. 
According to this, coulomb's law states that the amount of the electrostatic force 
of attraction between two point charges is directly proportional to the product of 
the charges' magnitudes and inversely proportional to the square of the distance 
between them formula. 
12
2
kq q
F
d
? 
 
Application of Ampere's Circuital Law: 
? The following are the principal applications of Ampere's circuital law: 
? The magnetic field produced by an infinitely long straight wire 
0
2
I
B
r
?
?
?? 
 
                                              
? The magnetic field due to conducting rod of radius R at a point at distance 
r from the rod 
2
,
2
o
I
r R B r
R
?
?
??
? ? ?
??
??
 
or Br ? 
 
Image: The magnetic field due to conducting rod 
a. If  rR ? (i.e., on the surface of the conducting rod) 
0
()
2
I
Bc
R
?
?
? r>R 
0
2
I
B
r
?
?
?? 
(i) The magnetic field due to hollow cylindrical pipe of radius R at a point at 
distance r from the current carrying hollow pipe. 
a. If rR ? , then 0 B ? 
b. If rR ? , then 
0
2
I
B
r
?
?
?? 
 
Force between two Parallel Current Carrying Conductor: 
? Two parallel linear conductors carrying currents in the same direction 
attract one another, while oppositely repelling each other. 
Page 5


 
                                              
Revision Notes 
Physics 
Moving Charges and Magnetism 
 
Electromagnetics: 
? Magnetic effects of electric current is a branch of physics that studies the 
influence of a magnetic field produced by a current or moving charge. 
 
Magnetic Field: 
? It is a region or place where the magnetic effect of a magnet, current 
carrying conductor, or moving charge can be felt. 
?  The tesla is the SI unit for it (T). 
 
Biot-Savart Law: 
? According to this law, " the magnetic flux density of which dB, is directly 
proportional to the length of the element dl, the current I, is given by 
2 0
2
sin
  Wb / m
4
idl
dB
r
? ?
?
? or tesla 
            
 
 
                                              
? 
0
3
4
id
dB
r
?
?
?
?
r
 
Here, 
0
? is a constant and it is called the permeability of free space and it 
is given as, 
7
0
4 10   Wb / A m ??
?
? ? ? 
 
Applications of Biot-Savart's Law 
? Biot-Savart law is used to calculate magnetic responses even at the atomic 
or molecular level. 
? Biot-Savart law is used in aerodynamic theory to calculate the velocity 
induced by vortex lines. 
 
Importance of Biot-Savart Law 
? Coulomb's law is similar to Biot-Savart law in electrostatics. 
? Biot-Savart law is also applicable for very small conductors carrying 
current. 
? Biot-Savart law is applicable for symmetrical current distribution. 
 
Rules to Find the Direction of Magnetic Field: 
? Right hand palm rule: The direction of the field will be perpendicular to 
the palm if we spread our right hand in such a way that the thumb is facing 
the direction of current and the fingers are facing the spot where we need 
to identify the direction of the field. 
? Maxwell's right handed screw rule: When the tip of a right-handed 
corkscrew moves in the direction of current flow through the conductor, 
the rotation of the screw's head gives the direction of magnetic lines of 
force. 
 
Ampere's Circuital Law: 
 
                                              
? Ampere's Circuital Law states that the line integral of the magnetic field 
around any closed path in vacuum is equal to 
0
? times the total current 
enclosed by the loop. 
             
0 net 
dI ? ??
?
B1 
? The simplified form of it is 
0 net 
BI ? ? , this equation is used in the following 
conditions. 
o At every point of the closed circuit B dl ? . 
o The magnetic field in the closed circuit is uniform at all points. 
 
Ampere's Law states that the magnetic field generated by an electric current is 
proportional to the size of the electric current. 
Gauss's law states that the electric flux through any closed surface is equal to the 
total charge inside divided by 
0
? . Charges are the source and sinks of the electric 
field. 
Biot-Savart's law states that the magnetic intensity at any point along an 
infinitely long straight wire caused by a constant current is exactly proportional 
to the current and inversely proportional to the distance between point and wire. 
According to this, coulomb's law states that the amount of the electrostatic force 
of attraction between two point charges is directly proportional to the product of 
the charges' magnitudes and inversely proportional to the square of the distance 
between them formula. 
12
2
kq q
F
d
? 
 
Application of Ampere's Circuital Law: 
? The following are the principal applications of Ampere's circuital law: 
? The magnetic field produced by an infinitely long straight wire 
0
2
I
B
r
?
?
?? 
 
                                              
? The magnetic field due to conducting rod of radius R at a point at distance 
r from the rod 
2
,
2
o
I
r R B r
R
?
?
??
? ? ?
??
??
 
or Br ? 
 
Image: The magnetic field due to conducting rod 
a. If  rR ? (i.e., on the surface of the conducting rod) 
0
()
2
I
Bc
R
?
?
? r>R 
0
2
I
B
r
?
?
?? 
(i) The magnetic field due to hollow cylindrical pipe of radius R at a point at 
distance r from the current carrying hollow pipe. 
a. If rR ? , then 0 B ? 
b. If rR ? , then 
0
2
I
B
r
?
?
?? 
 
Force between two Parallel Current Carrying Conductor: 
? Two parallel linear conductors carrying currents in the same direction 
attract one another, while oppositely repelling each other. 
 
                                              
? As a result, the force between two parallel current-carrying conductors per 
unit length is 
0 12
2
4
II
F
d
?
?
?? 
 
Magnetic Field of a Moving Point Charge: 
? The magnetic field due to a charge q , moving with speed v at a point P at 
a distance r from the charge is given by the following formula. 
0
2
()
4
q
B v r
r
?
?
? ? ? 
 
Force on a Moving Charge in Magnetic Field: 
? In a magnetic field, the force on a moving charge is given by  
? ? sin
m
F qvB q v B ? ? ? ? 
? where,  v ? magnitude of charge, B ? intensity of charge, and ? ? angle 
between direction of velocity and direction of magnetic field 
? Lorentz force is another name for it. 
o Neutral and big substances are affected by electromagnetic and 
gravitational forces. 
o The kinetic energy of a moving charge that moves perpendicular to the 
magnetic field remains constant. 
o The force that acts simultaneously in the presence of an electric and 
magnetic field. () F q E v B ? ? ? 
 
Rules to Find the Direction of Force: 
o The palm rule for the right hand: The fingertips of a linear conductor 
clasped in the palm of the right hand with the thumb pointing in the 
direction of the current will point in the direction of lines of force. 
o The rule of Fleming's left hand: If we spread our left hand's forefinger, 
middle finger, and thumb in such a way that they are perpendicular to each 
other, the first forefinger will represent the magnetic field, the second