Question

tic Waves The magnetic field in a plane monochromatic electromagnetic wave with wavelength A - 431 nm vacuum in the z-direction is described by B- (Bi sin(ks-t)(i +3) where B, -7.8x 1o* T, and i-hat and j-hat are the unit vectors in the .x and y directions, respectivety. 1) What is k, the wavenumber of this wave? 1.458e7 m Submit 2) What is Zmax the distance along the positive z-axis to the position where the magnitude of the magnetic field is a maximum at t 0 1.07e2 nm Submit 3) What is Emax, the amplitude of the electric field oscillations? 3309 V/m Submit 4) What is Ey, the y-component of the electric field at (x-o. у.0, 2+ Zmax) at t-o? 2339.81 V/m Submit

Number 6 only

Answer 1

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B vector = B_1 sin (kz - wt) (i^^+ j^^] wave is propagating in z-direction in vacuum So, Vertical-bar epsilon vector Vertical-bar = C. Vertical-bar B vector Vertical-bar Therefore Vertical-bar E vector Vertical-bar = c Vertical-bar B vector Vertical-bar & epsilon vector times B vector/ Vertical-bar epsilon vector times B Vertical-bar = k^^= z^^(2) Using (1) & (2) epsilon = C.B, sin (kz - wt) (i^^- j^^) Now at origin: z = x = y = 0, find epsilon_max epsilon = CB, sin (-wt) (i^^- j^^) To find epsilon_max: [sin (-wt)] should be maximum -sin (wt) should be maximum So, wt = 3 pi/2 = > t = 3 pi/2w w = 2 pi/lambda lambda = 43/nm = > t = 3 pi/2 times 431/2 pi t = 646.5 ns