Consider a plane, monochromatic, electromagnetic wave traveling in a homogeneous medium. Its magnetic field vector B in units of T is given by B₁ = 0 By = 0 B = Bo cos(9y + 2 x 10ºt) where y is in meter and t in second. a) Derive an expression for the electric field E associated with the magnetic field B. b) Find the direction of the the electric field E from part a. c) Calculate the average value of the Poynting vector in terms of Bo, and the speed of light. The index of refraction of the medium is n = 1.

A 0.102-A current is charging a capacitor that has square plates 4.20 cm on each side. The plate separation is 4.00 mm. a)  Find the time rate of change of electric flux between the plates. b) Find the displacement current between the plates.

The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B, = 510nT. What is the amplitude of the electric field part of the wave?

A sinusoidal electromagnetic wave is propagating in a vacuum in the +z-direction. Part A If at a particular instant and at a certain point in space the electric field is in the +x-direction and has a magnitude of 4.70 V/m, what is the magnitude of the magnetic field of the wave at this same point in space and instant in time? Express your answer in teslas. B = Π| ΑΣΦ ? T

For a certain electromagnetic wave in free space, at one instant the electric field vector points in the +z direction while the magnetic field vector points in the +x direction, as shown in the figure. In what direction is this wave traveling? B E +y +z +x -X -y

The magnetic field of an electromagnetic wave in a vacuum is B₂ = (2.6μT) sin((1.15 x 107) - wt), where x is in m and t is in S. You may want to review (Pages 889 -892). For help with math skills, you may want to review: Rearrangement of Equations Involving Multiplication and Division ▼ Part A What is the wave's wavelength? Express your answer to three significant figures and include the appropriate units. λ = Submit Part B f = Submit Part C MÅ Eo = Value What is the wave's frequency? Express your answer to three significant figures and include the appropriate units. Submit Request Answer μÀ Value Request Answer Units PHμÅ Value Request Answer Units ASSO What is the wave's electric field amplitude? Express your answer to two significant figures and include the appropriate units. 49999 Units ? AWYV ?

Suppose you have an electric field as a result of superposition of two waves given by Ē(z, t) = Eo cos(kz - wt) + Eo cos(kz + wt)â. a. Simplify Ē(z, t) as one term and find its associated magnetic field b. Find the instantaneous and time-averaged energy density.

There is a vector defined by John Henry Poynting in 1884 whose direction gives the direction that an electromagnetic wave transmits its field energy and whose magnitude is the rate at which energy is being transmitted per square meter of the wavefront. For mutually perpendicular E- and B-fields in the wave, the magnitude of the Poynting vector is S =EB/mu0 and the direction is given by a right-hand rule, curling fingers from E vector and B vector.  a) Carefully analyze the units of the Poynting vector and show that they are indeed watts per square meter.  b) Find the intensity of the light in a beam of light whose electric field strength is 360 N/C and whose magnetic field is 1.2 muT.

The energy flow to the earth from sunlight is about 1.40 kW/m2. Bmax

A plane electromagnetic wave is traveling in a vacuum. The magnetic field is directed along the z-axis and given by: B, = 3.0µT sin ((1.0 × 107 )x - (3.0 × 1015 )t ) a) Determine the wavelength , of the wave. b) What is the frequency, f, of the wave in Hertz? c) Determine the maximum strength of the B-field. d) Determine the maximum strength of the E-field and it direction. e) Can you find a time and place when the B-field is zero? f) What is the strength of the E-field when the B-filed is zero?