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www.GOALias.blogspot.comPhysicsHENDRIK ANTOON LORENTZ (1853 – 1928)134Hendrik Antoon Lorentz(1853 – 1928) Dutchtheoretical physicist,professor at Leiden. Heinvestigatedtherelationship betweenelectricity, magnetism, andmechanics. In order toexplain the observed effectof magnetic fields onemitters of light (Zeemaneffect), he postulated theexistence of electric chargesin the atom, for which hewas awarded the Nobel Prizein 1902. He derived a set oftransformation equations(known after him, asLorentz transformationequations) by some tangledmathematical arguments,but he was not aware thatthese equations hinge on anew concept of space andtime.E = Q ˆr / (4πε 0)r 2 (4.1)where ˆr is unit vector along r, and the field E is a vectorfield. A charge q interacts with this field and experiencesa force F given byF = q E = q Q ˆr / (4πε 0) r 2 (4.2)As pointed out in the Chapter 1, the field E is notjust an artefact but has a physical role. It can conveyenergy and momentum and is not establishedinstantaneously but takes finite time to propagate. Theconcept of a field was specially stressed by Faraday andwas incorporated by Maxwell in his unification ofelectricity and magnetism. In addition to depending oneach point in space, it can also vary with time, i.e., be afunction of time. In our discussions in this chapter, wewill assume that the fields do not change with time.The field at a particular point can be due to one ormore charges. If there are more charges the fields addvectorially. You have already learnt in Chapter 1 that thisis called the principle of superposition. Once the field isknown, the force on a test charge is given by Eq. (4.2).Just as static charges produce an electric field, thecurrents or moving charges produce (in addition) amagnetic field, denoted by B (r), again a vector field. Ithas several basic properties identical to the electric field.It is defined at each point in space (and can in additiondepend on time). Experimentally, it is found to obey theprinciple of superposition: the magnetic field of severalsources is the vector addition of magnetic field of eachindividual source.4.2.2 Magnetic Field, Lorentz ForceLet us suppose that there is a point charge q (movingwith a velocity v and, located at r at a given time t) inpresence of both the electric field E (r) and the magneticfield B (r). The force on an electric charge q due to both ofthem can be written asF = q [ E (r) + v × B (r)] ≡ F electric+F magnetic(4.3)This force was given first by H.A. Lorentz based on the extensiveexperiments of Ampere and others. It is called the Lorentz force. Youhave already studied in detail the force due to the electric field. If welook at the interaction with the magnetic field, we find the followingfeatures.(i)It depends on q, v and B (charge of the particle, the velocity and themagnetic field). Force on a negative charge is opposite to that on apositive charge.(ii) The magnetic force q [ v × B ] includes a vector product of velocityand magnetic field. The vector product makes the force due to magnetic