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-qo exp(-iot) Find the angular distribution of the radiation as well as the total power radiated...
4. Magnetic dipole radiation- two loops Consider a circular current loop in the xy plane of...
4. Magnetic dipole radiation- two loops
Consider a circular current loop in the xy plane of radius b as
in Section 11.1.3(See image above). Suppose there is another
parallel identical loop placed a distance d above the first loop.
The directions of the currents in the two loops are both
counterclockwise. The long wavelength approximation is
applicable.
(a) Compute the total vector potential A at positions in the
radiation zone.
(b) Compute the total magnetic field in the radiation zone....
The FM radio station KAMB broadcasts from an antenna atop a 170 meter tall radio tower at a frequency of 90 MHz with a total radiated power of 40 kilowatts. Neighbors have complained about problems th...
The FM radio station KAMB broadcasts from an antenna atop a 170
meter tall radio tower at a frequency of 90 MHz with a total
radiated power of 40 kilowatts. Neighbors have complained about
problems they attribute to excessive radiation from the tower, but
the city engineer who measured the radiation level near the base of
the tower found it to be well below the accepted standard. You have
been hired by the HOA to assess the engineer's report. You...
2. Dipole-dipole force The charge distribution where two equal but opposite charges are separated by a...
2. Dipole-dipole force The charge distribution where two equal but opposite charges are separated by a fixed distance a dipole and is very common and important in nature. Consider two dipoles, each consisting of charges ±q separated by a distance δ. The axes of two dipoles are parallel and their midpoints are separated by a distance r. One is inverted compared to the other. See the figure tq +9 (a) Calculate the force exerted on each dipole by the other...
Basic Coulomb's law tells us that the electric field of a point charge q, E=ke q/r2,...
Basic Coulomb's law tells us that the electric field of a point
charge q, E=ke q/r2, scales with distance r
as 1/r2: when the distance increases by a factor of 2,
the magnitude of the field decreases by a factor of 4. We can write
this as E(r) ∝ 1/r2. An interesting and practically
important question is how the electric field of a group of charges
scales with distance (asymptotically) far away from the group. The
figure below depicts 3...
When we find the electric field due to a continuous charge distribution, we imagine slicing that...
When we find the electric field due to a continuous charge distribution, we imagine slicing that source up into small pieces, finding the electric field produced by the pieces, and then integrating to find the electric field. Let's see what happens if we break a finite rod up into a small number of finite partides. The figure below shows a rod of length 2 carrying a uniform charge Q modeled as five particles of charge Q/5. Two particles are at...
question 2 added for reference; this is about question 3 2. Dipole-dipole force The charge distribution...
question 2 added for reference; this is about question 3
2. Dipole-dipole force The charge distribution where two equal but opposite charges are separated by a fixed distance δ is called a dipole and is very common and important in nature Consider two dipoles, each consisting of charges tq separated by a distance 6. The axes of two dipoles are parallel and their midpoints are separated by a distance r. One is inverted compared to the other. See the figure....
Electric potential for a continuous charge distribution: Let's consider a line of charge, of length L...
Electric potential for a continuous charge distribution: Let's consider a line of charge, of length L having a uniform charge density lambda = 10^-6 C/m and length L=10 cm. Find the electric potential at point P, which is at a distance Z=5 cm. above the midpoint of the line. where In is the natural logarithm. Consider two charged conducting spheres, radii r1 and r2, with charges q1 and q2, respectively. The spheres are far away from each other but connected...
Question 6 (5 marks) Two non-conducting spheres of equal radii R are placed adjacent to each...
Question 6 (5 marks) Two non-conducting spheres of equal radii R are placed adjacent to each other as shown in figure 5. Sphere 1 has a charge +91 distributed uniformly throughout its volume, and sphere 2 has charge +92 distributed uniformly throughout. A point P is chosen on the line joining the centers of the two spheres, at a distance R/2 from the centre of sphere 1 and 3R/2 from the centre of sphere 2. If the net electric field...
question 4-7 4. Travelling Waves and Their Characteristics A rope wave travels in the positive x -direction. You are also told that the speed of the wave is 1000 cm/s, its frequency is 200 H...
question 4-7
4. Travelling Waves and Their Characteristics A rope wave travels in the positive x -direction. You are also told that the speed of the wave is 1000 cm/s, its frequency is 200 Hz, and that the wave is subject to the following initial conditions: at x 0 and t = 0: y =-1 cm, and, at x = 0 and t : ar = +20 cm/s (this is the velocity of the point on the rope at horizontal...
1. Parallel plates. You have two equal but oppositely charged parallel conducting plates, separated by 10...
1. Parallel plates. You have two equal but oppositely charged parallel conducting plates, separated by 10 cm. A voltmeter shows that the potential difference between the plates is 500 V. (a) Which is at a higher potential, the positive or negative plate? (b) How big is the electric field between the plates? (c) You let go of an electron next to the negative plate. How much work does the electric field do in moving the electron to the positive plate?...
4. Magnetic dipole radiation- two loops
Consider a circular current loop in the xy plane of radius b as
in Section 11.1.3(See image above). Suppose there is another
parallel identical loop placed a distance d above the first loop.
The directions of the currents in the two loops are both
counterclockwise. The long wavelength approximation is
applicable.
(a) Compute the total vector potential A at positions in the
radiation zone.
(b) Compute the total magnetic field in the radiation zone....
The FM radio station KAMB broadcasts from an antenna atop a 170
meter tall radio tower at a frequency of 90 MHz with a total
radiated power of 40 kilowatts. Neighbors have complained about
problems they attribute to excessive radiation from the tower, but
the city engineer who measured the radiation level near the base of
the tower found it to be well below the accepted standard. You have
been hired by the HOA to assess the engineer's report. You...
2. Dipole-dipole force The charge distribution where two equal but opposite charges are separated by a fixed distance a dipole and is very common and important in nature. Consider two dipoles, each consisting of charges ±q separated by a distance δ. The axes of two dipoles are parallel and their midpoints are separated by a distance r. One is inverted compared to the other. See the figure tq +9 (a) Calculate the force exerted on each dipole by the other...
Basic Coulomb's law tells us that the electric field of a point
charge q, E=ke q/r2, scales with distance r
as 1/r2: when the distance increases by a factor of 2,
the magnitude of the field decreases by a factor of 4. We can write
this as E(r) ∝ 1/r2. An interesting and practically
important question is how the electric field of a group of charges
scales with distance (asymptotically) far away from the group. The
figure below depicts 3...
When we find the electric field due to a continuous charge distribution, we imagine slicing that source up into small pieces, finding the electric field produced by the pieces, and then integrating to find the electric field. Let's see what happens if we break a finite rod up into a small number of finite partides. The figure below shows a rod of length 2 carrying a uniform charge Q modeled as five particles of charge Q/5. Two particles are at...
question 2 added for reference; this is about question 3
2. Dipole-dipole force The charge distribution where two equal but opposite charges are separated by a fixed distance δ is called a dipole and is very common and important in nature Consider two dipoles, each consisting of charges tq separated by a distance 6. The axes of two dipoles are parallel and their midpoints are separated by a distance r. One is inverted compared to the other. See the figure....
Electric potential for a continuous charge distribution: Let's consider a line of charge, of length L having a uniform charge density lambda = 10^-6 C/m and length L=10 cm. Find the electric potential at point P, which is at a distance Z=5 cm. above the midpoint of the line. where In is the natural logarithm. Consider two charged conducting spheres, radii r1 and r2, with charges q1 and q2, respectively. The spheres are far away from each other but connected...
Question 6 (5 marks) Two non-conducting spheres of equal radii R are placed adjacent to each other as shown in figure 5. Sphere 1 has a charge +91 distributed uniformly throughout its volume, and sphere 2 has charge +92 distributed uniformly throughout. A point P is chosen on the line joining the centers of the two spheres, at a distance R/2 from the centre of sphere 1 and 3R/2 from the centre of sphere 2. If the net electric field...
question 4-7
4. Travelling Waves and Their Characteristics A rope wave travels in the positive x -direction. You are also told that the speed of the wave is 1000 cm/s, its frequency is 200 Hz, and that the wave is subject to the following initial conditions: at x 0 and t = 0: y =-1 cm, and, at x = 0 and t : ar = +20 cm/s (this is the velocity of the point on the rope at horizontal...
1. Parallel plates. You have two equal but oppositely charged parallel conducting plates, separated by 10 cm. A voltmeter shows that the potential difference between the plates is 500 V. (a) Which is at a higher potential, the positive or negative plate? (b) How big is the electric field between the plates? (c) You let go of an electron next to the negative plate. How much work does the electric field do in moving the electron to the positive plate?...
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