HANS CHRISTIAN OERSTED (1777–1851)

HANS CHRISTIAN OERSTED ( – ) * A dot appears like the tip of an arrow pointed at you, a cross is like the feathered tail of an arrow moving away from you. E = Q ˆ r / ( πε ) r ( . ) where ˆ r is unit vector along r , and the field E is a vector field. A charge q interacts with this field and experiences a force F given by F = q E = q Q ˆ r / ( πε ) r ( . ) As pointed out in the Chapter , the field E is not just an artefact but has a physical role. It can convey energy and momentum and is not established instantaneously but takes finite time to propagate. The concept of a field was specially stressed by Faraday and was incorporated by Maxwell in his unification of electricity and magnetism. In addition to depending on each point in space, it can also vary with time, i.e., be a function of time. In our discussions in this chapter, we will assume that the fields do not change with time. The field at a particular point can be due to one or more charges. If there are more charges the fields add vectorially. You have already learnt in Chapter that this is called the principle of superposition. Once the field is known, the force on a test charge is given by Eq. ( . ). Just as static charges produce an electric field, the currents or moving charges produce (in addition) a magnetic field, denoted by B (r) , again a vector field. It has several basic properties identical to the electric field. It is defined at each point in space (and can in addition depend on time). Experimentally, it is found to obey the principle of superposition: the magnetic field of several sources is the vector addition of magnetic field of each individual source . . . 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 (r) and the magnetic field B (r) . The force on an electric charge q due to both of them can be written as F = q [ E (r ) + v × B ( r )] ≡ F electric + F magnetic ( . ) This force was given first by H.A. Lorentz based on the extensive experiments of Ampere and others. It is called the Lorentz force . You have already studied in detail the force due to the electric field. If we look at the interaction with the magnetic field, we find the following features. (i) It depends on q , v and B (charge of the particle, the velocity and the magnetic field). Force on a negative charge is opposite to that on a positive charge. (ii) The magnetic force q [ v × B ] includes a vector product of velocity and magnetic field. The vector product makes the force due to magnetic