Question

(6%) Problem 3: The magnetic field of an electromagnetic wave is described by By = Bocos(kor - wt), where Bo = 2.5 x 10-6 T and w=2.5 107 rad/s. Randomized Variables Bo = 2.5 x 10-61 w=2.5 * 107 rad/s A 20% Part (a) What is the amplitude of the corresponding electric field oscillations, Eo, in terms of Bo? Eo=1 G D PO a 00 HOME B 0 d 7 TA 4 8 9 6 St A Во 5 с g 1 2 3 d i j + 0 END P m P t VO BACKSPACE CLEAR Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback. A 20% Part (b) Calculate the electric field Eo in volts per meter. A 20% Part (c) What is the frequency of the electromagnetic wave, f, in terms of @? A 20% Part (d) What is the wavelength of the electromagnetic wave, 1, in terms of w and the speed of light c? A 20% Part (e) Calculate the wavelength 1 in meters.

Answer 1

Part A.

Relation between electric field and magnetic field is given by:

In EM waves:

Electrostatic force due to electric field = Magnetic force

Fe = Fm

q*E0 = q*c*B0

E0 = c*B0

Where c = speed of light = 3.00*10^8 m/s

Part B.

Given that B0 = 2.5*10^-6 T

So,

E0 = 3.00*10^8*2.5*10^-6

E0 = 750 V/m = 7.50*10^2 V/m

Part C.

frequency of EM wave will be:

Angular frequency = w = 2*pi*f

f = w/(2*pi)

$f = \frac{\omega}{2 \pi}$

Part D.

Relation between frequency and wavelength is given by:

wavelength, $\lambda$ = c/f

$\lambda$ = c/(w/(2*pi)) = 2*pi*c/w

$\lambda = \frac{2 \pi c}{\omega}$

Part E.

Given that: w = 2.5*10^7 rad/sec

So,

$\lambda$ = 2*pi*3.00*10^8/(2.5*10^7) = 75.398 m

$\lambda$ = 75.4 m = wavelength

Let me know if you've any query.