A plane electromagnetic wave has a maximum electric field of 3 . 20 × 10 - 4 Vm - 1 . What is maximum magnetic field?

B 0 · C = E 0 B 0 = E 0 / c = 3 . 2 × 10 - 4 3 × 10 8 = 1 . 07 × 10 - 12 T B 0 = 1 . 07 × 10 - 12 T

In a plane EM wave, the magnetic field oscillates sinusoidally with a frequency of 2 . 0 × 10 10 Hz and an amplitude of 46 Wb m - 2 . Find the wavelength of the wave and the amplitude of the oscillating electric field.

(i) E → & B → have same frequency, wavelength and speed in plane. So, ν is same for both So, λ = c / ν = 3 × 10 8 2 × 10 10 = 1 . 5 × 10 - 2 m Wavelength of E → = 1 . 5 × 10 - 12 m (ii) B 0 C = E 0 E 0 = 46 × 3 × 10 8 = 138 × 10 8 v / m Amplitude of electric E 0 = 1 . 38 × 10 10 v / m .

In a plane EM wave, the electric field oscillates sinusoidally with a frequency of 2 × 10 10 Hz and an amplitude of 48 V m - 1 . Find the wavelength and the amplitude of the oscillating magnetic field.

(i) Wavelength of E → & B → will be same as they are in same is plane So , λ = C / ν = 3 × 10 8 2 × 10 10 = 1 . 5 × 10 - 2 m Wavelength of magnetic field = 1 . 5 × 10 - 2 m (ii) B 0 C = E 0 B 0 = E 0 / c = 48 3 × 10 8 = 16 × 10 - 8 T Amplitude of B → B 0 = 0 . 16 μT

A laser beam has intensity 2 . 5 × 10 14 W m - 2 . Find the amplitudes of electric and magnetic fields in the beam.

Average intensity I = 1 2 ∈ 0 E 2 · C E 2 = 2 I ∈ 0 C E = 2 × 2 . 5 × 10 14 8 . 85 × 10 - 12 × 3 × 10 8 = 0 . 434 × 10 9 V / m , Similarity intensity in terms of magnetic filed is I = 1 2 μ 0 CB 0 2 Or, we can use formula B 0 = E 0 c So, B 0 = 4 . 34 × 10 8 3 × 10 8 = 1 . 44 T B 0 = 1 . 44 T

In a plane electromagnetic wave, the amplitude of the magnetic field is 5 . 0 × 10 - 6 T. Find the amplitude of the electric field and the total average energy density of the wave.

Amplitude of the electric field E 0 = B 0 C = 5 × 10 - 6 × 3 × 10 8 = 15 × 10 2 V / m = 1 . 5 × 10 3 V / m Total Energy density E av = 1 2 ∈ 0 E 0 2 = 1 2 × 8 . 85 × 10 - 12 × 2 . 25 × 10 6 = 9 . 95 x 10 - 6 J m - 3 E av = 9 . 95 × 10 - 6 ≈ 1 × 10 - 5 J / m 3