2. (a) (b) () (d) (e) (f) SECTION B: ELECTROMAGNETISM Discuss why the concept of electric polarisation is useful. [3 marks] Show that the general vector identity Vx(xC)=-VC+((V.C) is true for the specific vector field C = z*2* E [3 marks] Gauss' law in electrostatics can be written in the form fldiz'f?mdmed 8 where the symbols have their usual meaning. Show that this equation is valid for a point charge @ at the centre of a sphere that surrounds it, and say why this integral equation can be useful. [3 marks| A friend's radio is a box of electronics which has a loop of metal poking out of it. The loop serves as part of the radio's receiver. Explain the role of the loop in the radio's receiver and how information can be transmitted to the radio. [3 marks] A new material discovered in Durham is found to be described by the dispersion relation given by k=3.0 x 107%w" +45.0 x 1075, where k is the wavevector and w is the angular frequency, and both & and w are in S.I. units. What percentage of the speed of light does a pulse of electromagnetic waves with central frequency 1.0 x 107 Hz travel through this material? [3 marks]| Write down the Maxwell equation that implies there are no magnetic monopoles. Explain how this equation can be tested experimentally. [3 marks|