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1. At t t 0, inertial systems S and S' are coincident in a region of electromagnetic field. After...
1. As observed by inertial systern S, an electrornagnetic plane wave of angular frequency ω is...
1. As observed by inertial systern S, an electrornagnetic plane wave of angular frequency ω is traveling in the +x direction through free space. Its electric and magnetic fields are given respectively by u(ut) E(z, y, z,t) = E0% cos (kz-at), B(z, y, z,t) =-e, cos(kz-wt) , where Eo is the electric-field amplitude and k-w/c is the magnitude of the propagation vector. Consider an inertial system S' that is moving with velocity Bcé, relative to inertial system S, where 0S...
1. A time-dependent electromagnetic field is given by, Ē(r,t = 0) = ĉEoe-(z/a)?, H (r,t=0) =...
1. A time-dependent electromagnetic field is given by, Ē(r,t = 0) = ĉEoe-(z/a)?, H (r,t=0) = 0 The field is located in vacuum, in an infinite three dimensional space. (a) Evaluate aĒ(r, t)/at and a (r, t)/at at t = 0. (b) Find the values of the fields, Ē(r, t) and H (r, t) for a general time t, satisfying ct >> a. (c) Sketch the fields found in (b) and interpret them physically.
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a...
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
. 3. An electromagnetic plane wave of (angular) frequency w is traveling in the r direc-...
. 3. An electromagnetic plane wave of (angular) frequency w is traveling in the r direc- tion through the vacuum. It is polarized in the y direction, and the amplitude of the electric field is E (a) Write down the electric and magnetic fields, E(r, y, z, t) and B(x, y, z,t). Be sure to define any auxiliaru quantities you introduce, in terms of w, Eo, and the con stants of nature.] (b) This same wave is observed from "other"...
3. Consider the electromagnetic wave k=(0.2) where .A Draw the electric field E, magnetic field B and Poynting vector S at the points = (x, y, z) that fulfill: a) th when t-0. - e condition-k = 0 Sid...
3. Consider the electromagnetic wave k=(0.2) where .A Draw the electric field E, magnetic field B and Poynting vector S at the points = (x, y, z) that fulfill: a) th when t-0. - e condition-k = 0 Side view 3D view b) the condition F. k-2 when t-o. Side view 3D view 3.B Calculate the wavelength λ of the wave (6). Compare the magnitude of λ with the magnitude of k. 3.C Wave (6) is expressed in terms of...
Number 6 only tic Waves The magnetic field in a plane monochromatic electromagnetic wave with wavelength...
Number
6 only
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...
1. (50 points) A plane electromagnetic (EM) wave, of angular frequency = 2Tx5.1x1014 rad/s, propagates inside...
1. (50 points) A plane electromagnetic (EM) wave, of angular frequency = 2Tx5.1x1014 rad/s, propagates inside a birefringent calcite crystal whose principal refractive indices are 1.65836 and ne- 1.48641 no Dt)= De.F-t) BF)-B.F) When using a given set of principal axes reference, the orientation of the wave-vector k is specified by k=(1, 1, 1)/ V3 As we know, when choosing an alternative and appropriate system of reference, the propagation of an ORDINARY wave and an EXTRAORDINARY wave of independent polarization...
1) A Hertzian dipole antenna is a short conducting wire carrying an approximately constant current over its length...
1) A Hertzian dipole antenna is a short conducting wire carrying an approximately constant current over its length If such a dipole is placed along the z-axis with its midpoint at the origin, and if the current flowing through it is i(t) ż lo cosot, assume I to be sufficiently small so that the observation point is approximately equidistant to all points on the dipole; that is, assume RR then the corresponding magnetic field is described by: olk2 sin e...
12-10. Car A starts from rest at t-0 and travels along a straight road with a...
12-10. Car A starts from rest at t-0 and travels along a straight road with a constant acceleration of 3 m/s until it reaches a speed of 27 m/s. Afterwards it maintains this speed. Also, when-0, car B located 2000 m down the road is traveling towards A at a constant speed of 20 m/s. Determine the distance travelled by car A when they pass each other. 20 m/s 2000 m 12-11. A particle travels along a straight line with...
Magnetic Fields from Two Infinite Sheets of Current 1 2 3 4 5 6 7 Two...
Magnetic Fields from Two Infinite Sheets of Current
1
2
3
4
5
6
7
Two infinite sheets of current flow parallel to the y-z plane as
shown. The sheets are equally spaced from the origin by
xo = 5.5 cm. Each sheet consists of an infinite array of
wires with a density n = 14 wires/cm. Each wire in the left sheet
carries a current I1 = 3.2 A in the negative
z-direction. Each wire in the right sheet...
1. As observed by inertial systern S, an electrornagnetic plane wave of angular frequency ω is traveling in the +x direction through free space. Its electric and magnetic fields are given respectively by u(ut) E(z, y, z,t) = E0% cos (kz-at), B(z, y, z,t) =-e, cos(kz-wt) , where Eo is the electric-field amplitude and k-w/c is the magnitude of the propagation vector. Consider an inertial system S' that is moving with velocity Bcé, relative to inertial system S, where 0S...
1. A time-dependent electromagnetic field is given by, Ē(r,t = 0) = ĉEoe-(z/a)?, H (r,t=0) = 0 The field is located in vacuum, in an infinite three dimensional space. (a) Evaluate aĒ(r, t)/at and a (r, t)/at at t = 0. (b) Find the values of the fields, Ē(r, t) and H (r, t) for a general time t, satisfying ct >> a. (c) Sketch the fields found in (b) and interpret them physically.
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
. 3. An electromagnetic plane wave of (angular) frequency w is traveling in the r direc- tion through the vacuum. It is polarized in the y direction, and the amplitude of the electric field is E (a) Write down the electric and magnetic fields, E(r, y, z, t) and B(x, y, z,t). Be sure to define any auxiliaru quantities you introduce, in terms of w, Eo, and the con stants of nature.] (b) This same wave is observed from "other"...
3. Consider the electromagnetic wave k=(0.2) where .A Draw the electric field E, magnetic field B and Poynting vector S at the points = (x, y, z) that fulfill: a) th when t-0. - e condition-k = 0 Side view 3D view b) the condition F. k-2 when t-o. Side view 3D view 3.B Calculate the wavelength λ of the wave (6). Compare the magnitude of λ with the magnitude of k. 3.C Wave (6) is expressed in terms of...
Number
6 only
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...
1. (50 points) A plane electromagnetic (EM) wave, of angular frequency = 2Tx5.1x1014 rad/s, propagates inside a birefringent calcite crystal whose principal refractive indices are 1.65836 and ne- 1.48641 no Dt)= De.F-t) BF)-B.F) When using a given set of principal axes reference, the orientation of the wave-vector k is specified by k=(1, 1, 1)/ V3 As we know, when choosing an alternative and appropriate system of reference, the propagation of an ORDINARY wave and an EXTRAORDINARY wave of independent polarization...
1) A Hertzian dipole antenna is a short conducting wire carrying an approximately constant current over its length If such a dipole is placed along the z-axis with its midpoint at the origin, and if the current flowing through it is i(t) ż lo cosot, assume I to be sufficiently small so that the observation point is approximately equidistant to all points on the dipole; that is, assume RR then the corresponding magnetic field is described by: olk2 sin e...
12-10. Car A starts from rest at t-0 and travels along a straight road with a constant acceleration of 3 m/s until it reaches a speed of 27 m/s. Afterwards it maintains this speed. Also, when-0, car B located 2000 m down the road is traveling towards A at a constant speed of 20 m/s. Determine the distance travelled by car A when they pass each other. 20 m/s 2000 m 12-11. A particle travels along a straight line with...
Magnetic Fields from Two Infinite Sheets of Current
1
2
3
4
5
6
7
Two infinite sheets of current flow parallel to the y-z plane as
shown. The sheets are equally spaced from the origin by
xo = 5.5 cm. Each sheet consists of an infinite array of
wires with a density n = 14 wires/cm. Each wire in the left sheet
carries a current I1 = 3.2 A in the negative
z-direction. Each wire in the right sheet...
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