## 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.## 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.

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,

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.

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 µ

µ

_{l }given by: Where l is the magnitude of the angular momentum of the circulating electron about the central nucleus. The smallest value of µ_{l }is called the**Bohr magneton**µ_{B}and it is given byµ

_{B}= 9.27×10^{–24}J/T
A moving coil galvanometer can be converted into a ammeter by introducing a shunt resistance r

_{s}, 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 |