1.Magnetic Force

Chapter 4: Moving charges and magnetism

Magnetic Force

What Is Magnetic Force?

If we place a point charge q in the presence of both a magnitude field given by magnitude B(r) and an electric field given by a magnitude E(r), then the total force on the electric charge q can be written as the sum of the electric force and the magnetic force acting on the object (Felectric + Fmagnetic ).

F = q E = q Q rˆ / (4πε0) r 2

Magnetic Field, Lorentz Force

Let us suppose that there is a point charge q (moving With a velocity v and, located at r at a given time t) in Presence of both the electric field E  and the magnetic Field B .The force on an electric charge q due to both of Them can be written as

F = q [ E  + v × B ] ≡ Felectric + Fmagnetic ).

MOTION IN A MAGNETIC FIELD
The force on a charged particle due to an electric field is directed parallel to the electric field vector in the case of a positive charge, and anti-parallel in the case of a negative charge. It does not depend on the velocity of the particle.
In contrast, the magnetic force on a charge particle is orthogonal to the magnetic field vector, and depends on the velocity of the particle. The right hand rule can be used to determine the direction of the force.
An electric field may do work on a charged particle, while a magnetic field does no work.
The Lorentz force is the combination of the electric and magnetic force, which are often considered together for practical applications.

MOTION IN COMBINED ELECTRIC AND MAGNETIC FIELDS
Lorentz Force
If the magnitudes of electric field strength and magnetic field strength are adjusted such that the magnitudes of the two forces are equal, then the net force acting on the charged particle is zero.
F = F(electric) + F(Magnetic) = q (E = v x B)
The below figure shows the representation of the electric field and the magnetic field along with the motion of charge when they are perpendicular to each other.

F(electric) = F(Magnetic)

In the figure, we can clearly observe that the magnetic forces and electric forces are in opposite directions to each other.

Cyclotron
A cyclotron is a machine used to accelerate charged particles or ions to high energies.
To enhance the energies of charged particles, cyclotron uses magnetic as well as electric fields. It is called crossed fields since the magnetic and electric fields are perpendicular to each other.

MAGNETIC FIELD DUE TO A CURRENT ELEMENT BIOT-SAVART LAW

Assume that a conductor of a very large length L is carrying current I through it. The magnetic field due to the current, B is perpendicular to the plane of the conductor. Further, let us assume that a section of this conductor, say dL is producing a section of the magnetic field dB at point r away from it in the same plane. Let the angle between dL and dB in the direction of r be Θ.

MAGNETIC FIELD ON THE AXIS OF A CIRCULAR CURRENT LOOP

2. Ampere's circuital law

THE SOLENOID AND THE TOROID

The solenoid

We shall discuss a long solenoid. By long solenoid we mean that thesolenoid’s length is large compared to its radius. It consists of a long wire wound in the form of a helix where the neighbouring turns are closely spaced. So each turn can be regarded as a circular loop. The net magnetic field is the vector sum of the fields due to all the turns. Enamelled wires are used for winding so that turns are insulated from each other.

Toroid?

A toroid is shaped like a solenoid bent into a circular shape such as to close itself into a loop-like structure. The toroid is a hollow circular ring, as can be seen in the image shown below, with many turns of enameled wire, closely wound with negligible spacing between any two turns.

FORCE BETWEEN TWO PARALLEL CURRENTS, THE AMPERE

The force between two long straight and parallel conductors separated by a distance r can be found by applying what we have developed in preceding sections. Figure 1 shows the wires, their currents, the fields they create, and the subsequent forces they exert on one another. Let us consider the field produced by wire 1 and the force it exerts on wire 2 (call the force F2). The field due to I1 at a distance r is given to be

What is a Moving Coil Galvanometer?

A moving coil galvanometer is an instrument which is used to measure electric currents. It is a sensitive electromagnetic device which can measure low currents even of the order of a few microamperes.

Moving-coil galvanometers are mainly divided into two types:

• Suspended coil galvanometer
• Pivoted-coil or Weston galvanometer

Moving Coil Galvanometer Principle

A current-carrying coil when placed in an external magnetic field experiences magnetic torque. The angle through which the coil is deflected due to the effect of the magnetic torque is proportional to the magnitude of current in the coil.