You measure the magnetic component of an electromagnetic wav

You measure the magnetic component of an electromagnetic wave and you find its wave function to be B^ right arrow (y, t) = (2.59 mu ?)cos((111 Mm^-1)y + (3.69 Ps^-1)t)i. What is the wave function for the electric component of this electromagnetic wave?

Solution

B = Bmax cos[ (2 pi / lambda) y + (2 pi f ) t ]

comparing with :

B = (2.59 uT) cos[ (111 x 10^6) y + (3.69 x 10^12) t ]

2 pi / lambda = 111 x 10^6

lambda = 5.66 x 10^-8 m

2 pi f = 3.69 x 10^12

f = 5.873 x 10^11 Hz

Speed = lambda x frequency = (5.66 x 10^-8 ) (5.873 x 10^11) = 33240.15 m/s

v B = E

33240.15 x 2.59 x 10^-6 = E

E = 0.086 V/m = 86.1 mV/m

E = 86.1 mV/m cos[ (111 x 10^6) y + (3.69 x 10^12) t ] (-k)