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d) (8 pts) Write an expression for a P-state ligthwave of angular frequency w and amplitude...
Two monochromatic plane waves are propagating in the xy-plane. Both plane waves have angular frequencyand amplitude...
Two monochromatic plane waves are propagating in the xy-plane. Both plane waves have angular frequencyand amplitude E0. First plane wave E1 is propagating along a line in the xy-plane at 45 degree to the x-axis and having its plane of vibration in the xy-plane. Second plane wave E2 is propagating along the x-axis and having its plane of vibration in the xz-plane. (a) Write the expressions for E1 and E2 assuming both fields are zero at t=0, x=0, y=0 and...
3. Interference on a screen (40 pts) Consider two plane wave beams propagating in free space....
3. Interference on a screen (40 pts) Consider two plane wave beams propagating in free space. They are identical except for the fact that they are misaligned with respect to each other by an angle 0, and are shined onto a screen. screen (a) If each beam has an amplitude Eo, write down an expression for the electric field of each plane wave in terms of Eo, the wavevector magnitude k, and the angular frequency w (using the coordinate system...
. 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"...
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...
Question 6 4 pts A rectangular loop rotates with a constant angular velocity w about one...
Question 6 4 pts A rectangular loop rotates with a constant angular velocity w about one of its sides as shown in the figure below in a uniform time-invariant magnetic field of flux density B. At t=0 the loop is the plane (x-z). The vector B is in the plane of drawing (y-z). With Eo being a positive constant and T = 21, the induced emf in the loop is of the following form: Question 7 4 pts If the...
A wave defined by the expression E (z,t) = A cos(ot-kz) fills all space directions perpendicular...
A wave defined by the expression E (z,t) = A cos(ot-kz) fills all space directions perpendicular to the z-axis in 3-dimensional space. A wave confined in the directions transverse to the direction of propagation can be constructed by superimposing such waves propagating in different directions. This problem is an illustration on how it can be done (a) Consider the space defined by the Cartesian coordinates x-y-z. Rotate the coordinates about the y-axis by an angle A to form a new...
8. (30) A plane electromagnetic direction. The electric polarization is parallel to i. The amplitude of...
8. (30) A plane electromagnetic direction. The electric polarization is parallel to i. The amplitude of the magnetic field is Bo. A rectangular loop of wire lies in the x-z plane, with edges lying at z-a/2, z=al2, -b12, and x -b/2. (a) Find the magnetic flux in the loop wave with wave vectork and frequency o travels in the z as a function of time. (Complex notation is easiest.) (b) Calculate the induced emf E in the loop as a...
The amplitude of 18.0 V/m field v ) Calculate the frequency of the wave. MHZ (b) Calculate the ma...
The amplitude of 18.0 V/m field v ) Calculate the frequency of the wave. MHZ (b) Calculate the magnetic freld B when the electric field has its maximum value in the negative y direction nT magnitude direction (c) write an expression for B with the correct unit vector, with numerical values for Bmax, , and w, and with its magnitude in the form in m and t in s.) (Assume B is measured in nT, x is magnitude direction c)...
A conducting bar of length D rotates with angular frequency w about a pivot P at...
A conducting bar of length D rotates with angular frequency w about a pivot P at one end of the bar (see the figure). The other end of the bar is in slipping contact with a stationary conducting wire in the shape of a circle (we only show a small part of that circle to keep the drawing simple). Between point P and the circular wire there is a resistor R as shown. Thus the bar, the resistor and the...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a f...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a function of frequency given by: I. Eo where co is radian frequency and o the "plasma frequency", which is assumed to be a constant related to the properties of the ionized gas. (a) 6 pts. Given the relation above, write an expression for the phase velocity in a plasma. (Assume μ-,-1). (b) 2 pts. Write an expression for the magnitude of...
Two monochromatic plane waves are propagating in the xy-plane. Both plane waves have angular frequencyand amplitude E0. First plane wave E1 is propagating along a line in the xy-plane at 45 degree to the x-axis and having its plane of vibration in the xy-plane. Second plane wave E2 is propagating along the x-axis and having its plane of vibration in the xz-plane. (a) Write the expressions for E1 and E2 assuming both fields are zero at t=0, x=0, y=0 and...
3. Interference on a screen (40 pts) Consider two plane wave beams propagating in free space. They are identical except for the fact that they are misaligned with respect to each other by an angle 0, and are shined onto a screen. screen (a) If each beam has an amplitude Eo, write down an expression for the electric field of each plane wave in terms of Eo, the wavevector magnitude k, and the angular frequency w (using the coordinate system...
. 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"...
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...
Question 6 4 pts A rectangular loop rotates with a constant angular velocity w about one of its sides as shown in the figure below in a uniform time-invariant magnetic field of flux density B. At t=0 the loop is the plane (x-z). The vector B is in the plane of drawing (y-z). With Eo being a positive constant and T = 21, the induced emf in the loop is of the following form: Question 7 4 pts If the...
A wave defined by the expression E (z,t) = A cos(ot-kz) fills all space directions perpendicular to the z-axis in 3-dimensional space. A wave confined in the directions transverse to the direction of propagation can be constructed by superimposing such waves propagating in different directions. This problem is an illustration on how it can be done (a) Consider the space defined by the Cartesian coordinates x-y-z. Rotate the coordinates about the y-axis by an angle A to form a new...
8. (30) A plane electromagnetic direction. The electric polarization is parallel to i. The amplitude of the magnetic field is Bo. A rectangular loop of wire lies in the x-z plane, with edges lying at z-a/2, z=al2, -b12, and x -b/2. (a) Find the magnetic flux in the loop wave with wave vectork and frequency o travels in the z as a function of time. (Complex notation is easiest.) (b) Calculate the induced emf E in the loop as a...
The amplitude of 18.0 V/m field v ) Calculate the frequency of the wave. MHZ (b) Calculate the magnetic freld B when the electric field has its maximum value in the negative y direction nT magnitude direction (c) write an expression for B with the correct unit vector, with numerical values for Bmax, , and w, and with its magnitude in the form in m and t in s.) (Assume B is measured in nT, x is magnitude direction c)...
A conducting bar of length D rotates with angular frequency w about a pivot P at one end of the bar (see the figure). The other end of the bar is in slipping contact with a stationary conducting wire in the shape of a circle (we only show a small part of that circle to keep the drawing simple). Between point P and the circular wire there is a resistor R as shown. Thus the bar, the resistor and the...
24 pts. Phase and group velocity of a plasma. The permittivity ε of a plasma (ionized gas) is a function of frequency given by: I. Eo where co is radian frequency and o the "plasma frequency", which is assumed to be a constant related to the properties of the ionized gas. (a) 6 pts. Given the relation above, write an expression for the phase velocity in a plasma. (Assume μ-,-1). (b) 2 pts. Write an expression for the magnitude of...
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