Electromagnetic Waves: Important Solved Problems

IMPORTANT SOLVED PROBLEMS

1. The electric field vector of a plane electromagnetic wave oscillates sinusoidal at a frequency 7.5×10¹⁰ Hz. Find the wave length of this wave.

Solution

Electric field vector frequency f = 7.5×10¹⁰ Hz

Given data

Formula:

 v = c/ λ      (or)      λ=c/v

λ = 3×10⁸ / 7.5×10¹⁰

λ = 0.4 / 100

λ = 4 / 1000

 λ = 4×10^‒3m

Wave length λ = 4 × 10⁻³ m

2. Electric field of plane electromagnetic wave is 450 NC^‒1. Find the magnetic field in wave.

Solution

Given data

Electric field vector E = 450 NC^‒1

Formula:

Magnetic field B = E/c

B = 450 / 3×10⁸

B = 150 / 10⁸

B =1.5×10^‒6 T

Magnetic field B = 1.5 × 10⁻⁶ Tesla

3. Amplitude of electric field in plane electromagnetic wave is 200NC^‒1 and its frequency is 7×10⁷ Hz. Determine the magnetic field amplitude and magnitude of wave vector.

Solution

Amplitude of electric field E = 200NC^‒1

Frequency v = 7×10⁷ Hz

Given data

Amplitude of magnetic field B = E/c

B = 200 / 3×10⁸

B = 66.6 / 10⁸

B = 6.6 × 10^‒7T

Magnitude of wave vector k = ω/c = 2πν / c

k = [ 2×3.14×7×10⁷ ] / [ 3×10⁸ ]

k = 43.96×10⁷ / 3×10⁸

k= 14.65 / 10

k=1.465

(i) Magnetic field B = 6.6. × 10^‒7 Telsa

(ii) Magnetude of wave vector k = 1.465

4. The magnetic field strength of an electromagnetic field is 5×10⁺⁶ T. Calculate the electric field strength if the wave is traveling in a medium in which the speed of the wave is 0.75c.

Solution

Given data

Magnetic field strength B = 5×10⁺⁶ T

Speed of the wave v=0.75 c

Electric field strength E=?

Formula:

Electric field strength E=vB

E=vB

E=0.75×3×10⁸×5×10^‒6

E=11.25×10²

E=1125 NC^‒1.

Electric field strength E = 1125 NC^‒1

5. Calculate the speed of the electromagnetic wave in a medium if the amplitude of electric and magnetic fields are 6 x 10⁴ NC^‒1 and 4× 10^‒4 T, respectively.

Solution

Given data

Amplitude of electric fields E₀ = 6 × 10⁴ N C^‒1

Amplitude of magnetic fields B₀ = 4 × 10^‒4 T

Speed of the electromagnetic wave in a medium v = ?

Formula:

Speed of EM wave in medium

v = E₀ / B₀

v = 6×10⁴ / 4×10^‒4

v = 1.5 × 10⁸ ms^‒1

Speed of EM wave in medium v = 1.5 × 10⁸ ms^‒1

ASSIGNMENT PROBLEMS

1. The electric field vector of a plane electromagnetic wave oscillates sinusoidal at a frequency 6.80 × 10¹⁰ Hz. Find the wave length of this wave. (Ans 4.4 × 10^‒9 m)

2. Electric field of plane electromagnetic wave is 500 NC^‒1 and the velocity of wave is 2.5 × 10⁸ meter per second. Find the magnetic field in wave. (Ans 2 × 10^‒4 T)