Question

Two travelling sinosoidal electromagnetic waves, each with an intensity 15 W/m2W/m2 , interfere to form a...

Two travelling sinosoidal electromagnetic waves, each with an intensity 15 W/m2W/m2 , interfere to form a standing wave. The resulting electric field E⃗ (z,t)E→(z,t) has nodes (i.e., is zero at all times) at z=…,−2a,−a,0,a,2a,…z=…,−2a,−a,0,a,2a,… with aaa = 4.0 mm , and satisifes E⃗ (z,0)=0E→(z,0)=0. Furthermore, the magnetic field B⃗ (z,t)B→(z,t) is observed to point along ±i^±i^ everywhere. You may take ccc = 3.0×108 m/sm/s and 8.9×10−12 F/mF/m .

A) What is the wavelength λλlambda of the two constituent travelling waves?

B) When will the electric field be zero everywhere for the first time after t=0? Express your answer in units of ns.

c)When will the magnetic field be zero everywhere for the first time after t=0

d)What is the amplitude (maximum magnitude) of the electric field for the standing wave? Express your answer in units of V/m.

e)How far from the origin is the nearest point where the amplitude of the (instantaneous) Poynting vector is maximum? Express your answer in units of meters.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A plane wave of wavelength 100 nm is polarized along z direction and travelling along -x...
A plane wave of wavelength 100 nm is polarized along z direction and travelling along -x direction with the electric field amplitude of 300 V/m (in vacuum). The maximum value of wave is at t=0 and x=0. Write the wave equation of magnetic field Calculate the intensity and Poynting vector of electromagnetic wave.
1) The average intensity of electromagnetic waves at a certain point is 500 W/m2. What is...
1) The average intensity of electromagnetic waves at a certain point is 500 W/m2. What is the amplitude of the wave's electric field. a. 265 V/m b. 449 V/m c. 614 V/m d. 736 V/m 2) What is the radiation momentum density of an electromagnetic wave having an electric field amplitude of 1000 V/m and travelling in a vacuum? a. 4.07 x 10^-15 kg m-2 s-1 b. 9.28 x 10^ -15 c. 1.48 x 10^-14 d. 6.25 x 10^-13 3)...
Consider an electromagnetic wave travelling in vacuum, where the electric field is given by: ?⃗ (?...
Consider an electromagnetic wave travelling in vacuum, where the electric field is given by: ?⃗ (? ,?)=40(?/?) sin[(8×106 ???/?) (?+??)+1.57 ???]?̂ a) Compute the: i. frequency ii. wavelength iii. period iv. amplitude v. phase velocity vi. direction of motion b) Write the corresponding expression for the magnetic field of this travelling wave (don’t forget to include the proper units). c) Plot this waveform as a function of x at t=0.
A plane monochromatic electromagnetic wave with wavelength λ = 4.9 cm, propagates through a vacuum. Its...
A plane monochromatic electromagnetic wave with wavelength λ = 4.9 cm, propagates through a vacuum. Its magnetic field is described by B⃗ =(Bxi^+Byj^)cos(kz+ωt) where Bx = 3.8 X 10-6 T, By = 3.2 X 10-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively. 1) What is f, the frequency of this wave? 2) What is I, the intensity of this wave? 3) What is Sz, the z-component of the Poynting vector at...
A plane monochromatic electromagnetic wave with wavelength λ = 3.2 cm, propagates through a vacuum. Its...
A plane monochromatic electromagnetic wave with wavelength λ = 3.2 cm, propagates through a vacuum. Its magnetic field is described by B⃗ =(Bxi^+Byj^)cos(kz+ωt)B→=(Bxi^+Byj^)cos⁡(kz+ωt) where Bx = 3.6 X 10-6 T, By = 4.4 X 10-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively. 1)What is f, the frequency of this wave? 2)What is I, the intensity of this wave? 3)What is Sz, the z-component of the Poynting vector at (x = 0,...
At one instant, the electric and magnetic fields at one point of an electromagnetic wave are...
At one instant, the electric and magnetic fields at one point of an electromagnetic wave are E⃗ =(210i^+340j^−60k^)V/mE→=(210i^+340j^−60k^)V/m and B⃗ =(7.1i^−8.0j^+ak^)B0B→=(7.1i^−8.0j^+ak^)B0. Part B What is the value of B0B0? Express your answer using two significant figures. B0 = μT Part C What is the Poynting vector at this time and position? Find the xx-component. Express your answer to two significant figures and include the appropriate units. Sx = Part D Find the yy-component. Express your answer to two significant figures...
Two waves traveling in opposite directions on a stretched rope interfere to give the standing wave...
Two waves traveling in opposite directions on a stretched rope interfere to give the standing wave described by the following wave function: y(x,t) = 4 sin⁡(2πx) cos⁡(120πt), where, y is in centimetres, x is in meters, and t is in seconds. The rope is two meters long, L = 2 m, and is fixed at both ends. In terms of the oscillation period, T, at which of the following times would all elements on the string have a zero vertical...
Deadline: 100% until Sunday, April 22 at 11:59 PM Electromagnetic Waves 2 1 2 3 4...
Deadline: 100% until Sunday, April 22 at 11:59 PM Electromagnetic Waves 2 1 2 3 4 1 6 A plane monochromatic electromagnetic wave with wavelength ? = 2.1 cm, propagates through a vacuum. Its magnetic field is described by B? =(Bxi^+Byj^)cos(kz+?t)B?=(Bxi^+Byj^)cos?(kz+?t) where Bx = 2 X 10-6 T, By = 4.9 X 10-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively. 1) What is f, the frequency of this wave?GHz You currently...
A plane electromagnetic wave varies sinusoidally at 98.2 MHz as it travels through vacuum along the...
A plane electromagnetic wave varies sinusoidally at 98.2 MHz as it travels through vacuum along the positive x direction. The peak value of the electric field is 2.10 mV/m, and it is directed along the positive y direction. (a) Find the wavelength. m (b) Find the period. ns (c) Find the maximum value of the magnetic field. pT (d) Write expressions in SI units for the space and time variations of the electric field. (x is in meters, and t...
1) 2 point charges are separated by a distance of 8 cm. The left charge is...
1) 2 point charges are separated by a distance of 8 cm. The left charge is 48 mC and the right charge is -16mC. Using a full sheet of paper: draw the 2 charges separated by 8cm, centered in the sheet. (if you are missing a ruler estimate 8cm as ⅓ a paper sheet length). [6] a) Draw field lines to indicate the electric fields for this distribution. [4] b) Draw 3 equipotential surfaces, 1 each, that pass: -Through the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT