Consider a charge, q, rotating about the origin in the x–y plane at a radius, a,...
Consider a charge, q, rotating about the origin in the x–y plane at a radius, a, with angular frequency ω.
Find the electric dipole, electric quadrupole, and magnetic dipole vector potentials in the radiation zone for this charge distribution.
Please to show all of your step, thank!
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Consider a charge, q, rotating about the origin in the x–y plane
at a radius, a,...
A charge q is moving in a circle in the x-y plane with frequency w. Find...
A charge q is moving in a circle in the x-y plane with frequency w. Find the electric dipole vector potential in the radiation zone. Find the electric quadrupole vector potential in the radiation zone. Find the magnetic dipole vector potential in the radiation zone. Please show every step. Thanks!
For a charge e rotating in the x-y plane at radius a and angular speed w,...
For a charge e rotating in the x-y plane at radius a and angular
speed w, show that there is only a z component of radiated angular
momentum with magnitude dLz/dt=e²k³a²/6πϵ₀. What about a charge
oscillating along the z axis?
For a charge e rotating in the x-y plane at radius a and angular speed w, show that there is only a z component of radiated angular momentum with mag- nitude dLz/dt = e2kw6πε0, what about a charge oscillating along...
Problem 3. An electric dipole of magnitude Po is placed at the origin and rotates clockwise...
Problem 3. An electric dipole of magnitude Po is placed at the origin and rotates clockwise in the xy -plane with the angular frequency o.Find the electric and magnetic fields in the radiation zone and calculate the Poynting vector.
Quadrupole charge distribution. Consider the four-charge distribution in the xy- plane along the x-axis, the y-axis,...
Quadrupole charge distribution. Consider the four-charge distribution in the xy- plane along the x-axis, the y-axis, and in the x = y direction for positive charges at a (1,1), a (-1,-1) and negative charges at a (11) and a (-1,1). Take the absolute value of the charges to be the same and equal to q. a) Recall in class we found that for the dipole charge distribution there are two axes of symmetry defined to be straight lines to which...
(a) A ring (in y-z plane) of radius R, mass M, with uniform charge Q is...
(a) A ring (in y-z plane) of radius R, mass M, with uniform charge Q is rotated about its axis (x-axis) as shown. Derive an expression for the magnetic dipole momentů for this ring. Express ŭ in terms of the angular momentum, 1o , of the ring (standard form). (6) Using the result of part (a) write down an expression for the magnetic dipole moment of the ring shown in Fig (6) (the axis of this ring is în which...
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....
8. (3) A ring with charge Q and radius R is in the x-y plane and...
8. (3) A ring with charge Q and radius R is in the x-y plane and is centered on the origin. Derive an expression for the electric potential at a point P on the z-axis a distance z above the x-y plane Please also indicate how much energy it would take to bring a charge q from far away and place it at point P
A total charge of Q is uniformly distributed around the perimeter of a circle with radius a in the x-y plane centered at origin as shown in Figure P4
1. A total charge of Q is uniformly distributed around the perimeter of a circle with radius a in the x-y plane centered at origin as shown in Figure P4. (a) Find the electric field at all points on the z axis, i.e., (0,0,z). (b) Use the result you obtain in (a) to find the electric field of an infinite plane of charge with surface charge density ps located at the x-y plane. 2. Find the electric field due to a...
A Cycloidal Path A particle with mass m and positive charge q starts from rest at the origin as s...
Please help, I am
struggling!
A Cycloidal Path A particle with mass m and positive charge q starts from rest at the origin as shown in the figure below. There is a uniform electric field = Eo? and a uniform magnetic field B = BoZ The path of the charged sketched below is a cycloid whose radius of curvature at the top points is twice the y-coordinate at that level. This path is exactly the same as the path of...
1. *A thin disc of radius a and height h contains charge +q uniformly distributed throughout the disc. The disc lies in...
1. *A thin disc of radius a and height h contains charge +q uniformly distributed throughout the disc. The disc lies in the ry-plane, is located with its centre at the origin, and rotates about the z-axis with angular velocity -w (a) Using cylindrical coordinates (s , z), specify the current density J(s φ z) as a func- tion of position. Find the magnetic dipole moment Hint: After you have determined the volume current density, you can use this result...
For a charge e rotating in the x-y plane at radius a and angular
speed w, show that there is only a z component of radiated angular
momentum with magnitude dLz/dt=e²k³a²/6πϵ₀. What about a charge
oscillating along the z axis?
For a charge e rotating in the x-y plane at radius a and angular speed w, show that there is only a z component of radiated angular momentum with mag- nitude dLz/dt = e2kw6πε0, what about a charge oscillating along...
Problem 3. An electric dipole of magnitude Po is placed at the origin and rotates clockwise in the xy -plane with the angular frequency o.Find the electric and magnetic fields in the radiation zone and calculate the Poynting vector.
Quadrupole charge distribution. Consider the four-charge distribution in the xy- plane along the x-axis, the y-axis, and in the x = y direction for positive charges at a (1,1), a (-1,-1) and negative charges at a (11) and a (-1,1). Take the absolute value of the charges to be the same and equal to q. a) Recall in class we found that for the dipole charge distribution there are two axes of symmetry defined to be straight lines to which...
(a) A ring (in y-z plane) of radius R, mass M, with uniform charge Q is rotated about its axis (x-axis) as shown. Derive an expression for the magnetic dipole momentů for this ring. Express ŭ in terms of the angular momentum, 1o , of the ring (standard form). (6) Using the result of part (a) write down an expression for the magnetic dipole moment of the ring shown in Fig (6) (the axis of this ring is în which...
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....
8. (3) A ring with charge Q and radius R is in the x-y plane and is centered on the origin. Derive an expression for the electric potential at a point P on the z-axis a distance z above the x-y plane Please also indicate how much energy it would take to bring a charge q from far away and place it at point P
Please help, I am
struggling!
A Cycloidal Path A particle with mass m and positive charge q starts from rest at the origin as shown in the figure below. There is a uniform electric field = Eo? and a uniform magnetic field B = BoZ The path of the charged sketched below is a cycloid whose radius of curvature at the top points is twice the y-coordinate at that level. This path is exactly the same as the path of...
1. *A thin disc of radius a and height h contains charge +q uniformly distributed throughout the disc. The disc lies in the ry-plane, is located with its centre at the origin, and rotates about the z-axis with angular velocity -w (a) Using cylindrical coordinates (s , z), specify the current density J(s φ z) as a func- tion of position. Find the magnetic dipole moment Hint: After you have determined the volume current density, you can use this result...
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