# Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is v = 50.0 MHz. (a) Determine, B0, ω, k, and λ. (b) Find expressions for E and B. - Physics

Numerical

Suppose that the electric field amplitude of an electromagnetic wave is E0 = 120 N/C and that its frequency is v = 50.0 MHz.

(a) Determine, B0, ω, k, and λ.

(b) Find expressions for E and B.

#### Solution

Electric field amplitude, E0 = 120 N/C

Frequency of source, v = 50.0 MHz = 50 × 106 Hz

Speed of light, c = 3 × 10m/s

(a) Magnitude of magnetic field strength is given as:

"B"_0 = "E"_0/"c"

= 120/(3 xx 10^8)

= 4 × 10−7 T

= 400 nT

Angular frequency of source is given as:

ω = 2πv

= 2π × 50 × 106

Propagation constant is given as:

"k" = ω/"c"

= (3.14 xx 10^8)/(3 xx 10^8)

Wavelength of wave is given as:

lambda = "c"/"v"

= (3 xx 10^8)/(50 xx 10^6)

= 6.0 m

(b) Suppose the wave is propagating in the positive x-direction. Then, the electric field vector will be in the positive y-direction and the magnetic field vector will be in the positive z-direction. This is because all three vectors are mutually perpendicular.

Equation of electric field vector is given as:

vec"E" = "E"_0 sin ("k""x" - ω"t")hat"j"

= 120 sin [1.05"x" - 3.14 xx 10^8"t"]hat"j"

And, magnetic field vector is given as:

vec"B" = "B"_0 sin ("kx" - ω"t")hat"k"

vec"B" = (4 xx 10^-7) sin [1.05"x" - 3.14 xx 10^8"t"]hat"k"

Concept: Electromagnetic Waves
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#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 8 Electromagnetic Waves
Exercise | Q 8.8 | Page 286
NCERT Class 12 Physics Textbook
Chapter 8 Electromagnetic Waves
Exercise | Q 8 | Page 286

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