com www.GOALias.blogspot.com

www.GOALias.blogspot.comPhysicsdrift velocity v d(see Chapter 3). In the presence of an external magneticfield B, the force on these carriers is:F = (nAl)q v d× Bwhere q is the value of the charge on a carrier. Now nqv dis the currentdensity j and |(nq v d)|A is the current I (see Chapter 3 for the discussionof current and current density). Thus,F = [(nqev d)Al] × B = [ jAl ] × B= I1 × B (4.4)where l is a vector of magnitude l, the length of the rod, and with a directionidentical to the current I. Note that the current I is not a vector. In the laststep leading to Eq. (4.4), we have transferred the vector sign from j to l.Equation (4.4) holds for a straight rod. In this equation, B is the externalmagnetic field. It is not the field produced by the current-carrying rod. Ifthe wire has an arbitrary shape we can calculate the Lorentz force on itby considering it as a collection of linear strips dl jand summingF = ∑ I l ×Bjd jThis summation can be converted to an integral in most cases.ON PERMITTIVITY AND PERMEABILITYIn the universal law of gravitation, we say that any two point masses exert a force oneach other which is proportional to the product of the masses m 1, m 2and inverselyproportional to the square of the distance r between them. We write it as F = Gm 1m 2/r 2where G is the universal constant of gravitation. Similarly in Coulomb’s law of electrostaticswe write the force between two point charges q 1, q 2, separated by a distance r asF = kq 1q 2/r 2 where k is a constant of proportionality. In SI units, k is taken as1/4πε where ε is the permittivity of the medium. Also in magnetism, we get anotherconstant, which in SI units, is taken as µ/4π where µ is the permeability of the medium.Although G, ε and µ arise as proportionality constants, there is a difference betweengravitational force and electromagnetic force. While the gravitational force does not dependon the intervening medium, the electromagnetic force depends on the medium betweenthe two charges or magnets. Hence while G is a universal constant, ε and µ depend onthe medium. They have different values for different media. The product εµ turns out tobe related to the speed v of electromagnetic radiation in the medium through εµ =1/ v 2 .Electric permittivity ε is a physical quantity that describes how an electric field affectsand is affected by a medium. It is determined by the ability of a material to polarise inresponse to an applied field, and thereby to cancel, partially, the field inside the material.Similarly, magnetic permeability µ is the ability of a substance to acquire magnetisation inmagnetic fields. It is a measure of the extent to which magnetic field can penetrate matter.136EXAMPLE 4.1Example 4.1 A straight wire of mass 200 g and length 1.5 m carriesa current of 2 A. It is suspended in mid-air by a uniform horizontalmagnetic field B (Fig. 4.3). What is the magnitude of the magneticfield?