MOVING CHARGES AND MAGNETISM
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.
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
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.
is the net current enclosed by the closed circuit.
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 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.
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
where φ is the equilibrium deflection and k the torsion constant of the spring.
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
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 µl is called the Bohr magneton µB and it is given by
µB = 9.27×10–24 J/T
Where l is the magnitude of the angular momentum of the circulating electron about the central nucleus. The smallest value of µl is 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 |