Lorentz force:

The total force on a charge q moving with velocity v in the presence of magnetic and electric fields B and E, respectively is called the Lorentz force. It is given by the expression: F = q (v × B + E). The magnetic force q (v × B) is normal to v and work done by it is zero.

cyclotron frequency:

In a uniform magnetic field B, a charge q executes a circular orbit in a plane normal to B. Its frequency of uniform circular motion is called the cyclotron frequency and is given by: This frequency is independent of the particle’s speed and radius.

Biot-Savart law:

The Biot-Savart law asserts that the magnetic field dB due to an element dl carrying a steady current I at a point P at a distance r from the current element is:

The magnitude of the magnetic field due to a circular coil

The magnitude of the magnetic field due to a circular coil of radius R carrying a current I at an axial distance ‘x’ from the centre is At the center this reduces to

Ampere’s Circuital Law:

Let an open surface S be bounded by a loop C. Then the Ampere’s law states that
where I refers to the current passing through S.
  • If B is directed along the tangent to every point on the perimeter L of a closed curve and is constant in magnitude along perimeter then,
is the net current enclosed by the closed circuit.
The magnitude of the magnetic field at a distance R from a long, straight wire carrying a current I is given by: The field lines are  concentric circles with the wire.
The magnitude of the field B inside a long solenoid carrying a current I is

where n is the number of turns per unit length. For a toroid one obtains,

Where N is the total number of turns and r is the average radius.
A planar loop carrying a current I, having N closely wound turns, and an area A possesses a magnetic moment m where,
m = N I A
  • And the direction of m is given by the right-hand thumb rule: curl the palm of your right hand along the loop with the fingers pointing in the direction of the current. The thumb sticking out gives the direction of m (and A)
  • When this loop is placed in a uniform magnetic field B, the force F on it is: F = 0
  • And the torque on it is,
  • In a moving coil galvanometer, this torque is balanced by a countertorque due to a spring, yielding
kφ = NI AB
where φ is the equilibrium deflection and k the torsion constant of the spring.
An electron moving around the central nucleus has a magnetic moment µl given by: Where l is the magnitude of the angular momentum of the circulating electron about the central nucleus. The smallest value of µis called the Bohr magneton µB and it is given by
µB = 9.27×10–24 J/T
A moving coil galvanometer can be converted into a ammeter by introducing a shunt resistance rs, of small value in parallel. It can be converted into a voltmeter by introducing a resistance of a large value in series.

List of Topics​

Magnetic force Magnetic sources and fields
Lorentz Force
Current carrying conductor
Motion in a magnetic field Nature of trajectories
Derivation of radius and angular frequency of circular motion of a charge in uniform magnetic field
Motion in magnetic and electrical field combined  velocity selector
Cyclotron: Principle, working and construction
Biot–savart law Current element
Magnetic field on circular current loop
Right hand thumb rule to find direction
Ampere’s circuital law Statement ,explanation and applications
The magnetic field due to an infinitely long straight current carrying wire
Solenoid and toroid
The ampere
Current loop Torque on rectangular current loop
Circular current loop as a magnetic dipole
Magnetic dipole moment of a revolving electron
Gyro magnetic Ratio
Moving coil galvanometer Current sensitivity and voltage sensitivity
Conversion of galvanometer to ammeter and voltmeter
Numericals Concept based problems