• The energy density (energy per

• The energy density (energy per unit volume) associated with an electromagnetic wave propagating in vacuum or free space is u ε µ   where v dx dt is the velocity of the loop. This emf is known as motional emf since it is produced due to the movement of the loop in the magnetic field. From Lenz’s law, it is found that the induced current flows in clockwise direction. If R is the resistance of the loop, then the induced current is given by = ε Bl v  (A4. ) A4. ANALOGIES BETWEEN LC OSCILLATIONS AND SIMPLE HARMONIC OSCILLATIONS Quantitative treatment The mechanical energy of the spring- mass system is given by mv k x  (A4. ) The energy E remains constant for varying values of x and v . Differentiating E with respect to time, we get dE dt v dv dt k x dx dt      +      = or m d x dt kx =  (A4. ) since dx dt v and dv dt d x dt This is the differential equation of the oscillations of the spring-mass system. The general solution of equation ( . ) is of the form x t X t ( ) cos ω f  (A4. ) - - - - Appendix where, ε  E u E is the energy density in an electric field and µ B u B is the energy density in a magnetic field. Since, E = Bc ⇒ u B = u E .