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Q-2) The infinitely long cylinder volume r < a carries a steady electric current of unknown density JAmps/m2) oriented through z direction = Jêz) as shown in the figure. There is no current outsid...
Problem 4, 30 marks The infinitely long conducting cylinder of radius R carries the volume current...
Problem 4, 30 marks The infinitely long conducting cylinder of radius R carries the volume current density directed along its axis whose absolute value is a cubic function of the distance from the center of the cylinder r, j(r)-br3, where b is a known constant. a. Find the magnitude and direction of the magnetic field B forr>R. b. Find the magnitude and direction of the magnetic field B for r<R. c. Imagine that the conductor has magnetic permeability H (5...
A long, straight, solid cylinder, oriented with its axis in the z−direction, carries a current whose...
A long, straight, solid cylinder, oriented with its axis in the z−direction, carries a current whose current density is J⃗ . The current density, although symmetrical about the cylinder axis, is not constant but varies according to the relationship J⃗ =2I0πa2[1−(ra)2]k^forr≤a=0forr≥a where a is the radius of the cylinder, r is the radial distance from the cylinder axis, and I0 is a constant having units of amperes. A)Using Ampere's law, derive an expression for the magnitude of the magnetic field...
An infinitely long, straight conductor with a circular cross-section of radius b carries a steady current I. (a) Determine the magnetic flux density (B) both inside and outside the conductor. (b) Det...
An infinitely long, straight conductor with a circular cross-section of radius b carries a steady current I. (a) Determine the magnetic flux density (B) both inside and outside the conductor. (b) Determine the vector magnetic potential (A) both inside and outside the conductor from the relationship B V x A
An infinitely long, straight conductor with a circular cross-section of radius b carries a steady current I. (a) Determine the magnetic flux density (B) both inside and outside the conductor....
Consider an infinitely long cylinder of radius R with two spherical cavities, also of radius R....
Consider an infinitely long cylinder of radius R with two
spherical cavities, also of radius R. The cylinder carries a
uniform volume charge density of ρ. There are two point charges at
the center of the spherical cavities both of charge q.
Hint: Just as the previous hint, superposition is your friend. A
suggestion is to find the contributions from the cylinder and
spheres separately.
(a) Find the electric field at the points A, B, and C in the
diagram...
5. An infinitely long cylinder of radius R carries a frozen-in" magietization parallel to z-axis and...
5. An infinitely long cylinder of radius R carries a frozen-in" magietization parallel to z-axis and is given by M = ksi, where k is a constant and s is the distance from the axis. There is no free current anywhere. Find the magnetic field inside and outside the cylinder.
Problem 3: An infinitely long solid cylinder of radius 2 m along the z-axis carries a...
Problem 3: An infinitely long solid cylinder of radius 2 m along the z-axis carries a volume current density of in the z-Direction. An infinitely long current filament at y 5 m in the x-z plane carried a current of A in the -z direction. Find the force per unit length on the filament.
(2) 4.[4pts) An infinitely long cylinder of radius R carries NO free current but magnetization M=ks,...
(2) 4.[4pts) An infinitely long cylinder of radius R carries NO free current but magnetization M=ks, where k > 0 is a constant and s is the cylindrical radius from the axis. Find the magnetic field B due to M both inside and outside of the cylinder.
Question 3: A long hollow cylinder with radius R carries a time-dependent surface current density K(t)...
Question 3: A long hollow cylinder with radius R carries a time-dependent surface current density K(t) = Kosin(wt) $ (see figure below). The current K(t) varies slowly enough that we are still in the quasistatic approximation. (15 points) KO a) Find the magnetic field B(1), magnitude and direction inside and outside the cylinder. (4 points) b) Find the induced electric field E(t), magnitude and direction, inside and outside the cylinder (8 points) c) Find the displacement current Jinside and outside...
Long charged cylinder A long cylinder with radius R carries a volume charge density S. a)...
Long charged cylinder A long cylinder with radius R carries a volume charge density S. a) Find the direction of the electric field E produced by the cylinder? b) Find E(r) for r less than R, where r is the perpendicular distance from the cylinder axis. c) Find E(R) for r greater than R d) plot E(r) for 0 leqr less than infinity e) Is the answer to part (c) consistent with the result for an infinite line of charge?
An infinitely long insulating cylinder of radius R has a volume charge density that varies with...
An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as p po (a-where po a and b are positive constants and ris the distance from the axis of the cylinder. Use Gauss's law to determine the magnitude of the electric field at radial distances (a) r< R and (b)r>R
Problem 4, 30 marks The infinitely long conducting cylinder of radius R carries the volume current density directed along its axis whose absolute value is a cubic function of the distance from the center of the cylinder r, j(r)-br3, where b is a known constant. a. Find the magnitude and direction of the magnetic field B forr>R. b. Find the magnitude and direction of the magnetic field B for r<R. c. Imagine that the conductor has magnetic permeability H (5...
An infinitely long, straight conductor with a circular cross-section of radius b carries a steady current I. (a) Determine the magnetic flux density (B) both inside and outside the conductor. (b) Determine the vector magnetic potential (A) both inside and outside the conductor from the relationship B V x A
An infinitely long, straight conductor with a circular cross-section of radius b carries a steady current I. (a) Determine the magnetic flux density (B) both inside and outside the conductor....
Consider an infinitely long cylinder of radius R with two
spherical cavities, also of radius R. The cylinder carries a
uniform volume charge density of ρ. There are two point charges at
the center of the spherical cavities both of charge q.
Hint: Just as the previous hint, superposition is your friend. A
suggestion is to find the contributions from the cylinder and
spheres separately.
(a) Find the electric field at the points A, B, and C in the
diagram...
5. An infinitely long cylinder of radius R carries a frozen-in" magietization parallel to z-axis and is given by M = ksi, where k is a constant and s is the distance from the axis. There is no free current anywhere. Find the magnetic field inside and outside the cylinder.
Problem 3: An infinitely long solid cylinder of radius 2 m along the z-axis carries a volume current density of in the z-Direction. An infinitely long current filament at y 5 m in the x-z plane carried a current of A in the -z direction. Find the force per unit length on the filament.
(2) 4.[4pts) An infinitely long cylinder of radius R carries NO free current but magnetization M=ks, where k > 0 is a constant and s is the cylindrical radius from the axis. Find the magnetic field B due to M both inside and outside of the cylinder.
Question 3: A long hollow cylinder with radius R carries a time-dependent surface current density K(t) = Kosin(wt) $ (see figure below). The current K(t) varies slowly enough that we are still in the quasistatic approximation. (15 points) KO a) Find the magnetic field B(1), magnitude and direction inside and outside the cylinder. (4 points) b) Find the induced electric field E(t), magnitude and direction, inside and outside the cylinder (8 points) c) Find the displacement current Jinside and outside...
An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as p po (a-where po a and b are positive constants and ris the distance from the axis of the cylinder. Use Gauss's law to determine the magnitude of the electric field at radial distances (a) r< R and (b)r>R
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