The wavelength of an electromagnetic wave is 6 mm. The electric field in that y direction and its maximum amplitude is ` 33 Vm^(-1) ` write the equation for electric and magnetic fields as function of x and t.

Explanation

Wavelength ` lamda = 6 mm = 6 xx 10 ^(-3) m `
Electric field ` E_0 = 33 Vm ^(-1) `
Magnetic field ` B_0 = (E_0)/(C ) `
Angular frequency `omega = 2 pi upsilon `
` omega = 2pi xx (C )/(lamda ) , " "[ because C = 3 xx 10 ^8 m//s] `
` omega = 2 xx 3.14 xx (3xx 10 ^(8))/( 6 xx 10 ^(-3)) `
` = 3.14 xx 10 ^(11) rad//s `
` therefore ` The amplitude of magnetic field
` B_0 = (E_0)/(C) `
` B_0 = (33)/( 3 xx 10 ^(8)) = 11 xx 10^(-8 ) T `
The equation for the electric field along ` y` - axis in the electromagnetic wave is
` E_y = E_0 sin omega (t - (x)/(c) ) `
` Ey = 33 sin pi xx 10 ^(11) (t - (x)/(c)) `
In the electromagnetic wave the equation for the magnetic field is
` B_2 = B_0 sin omega ( t - (x)/(c)) `
` B_2 = 11 xx 10 ^(-8) xx sin pi xx 10 ^(11) (t - (x)/(c)) `