a) Consider a uniformly dense sphere of radius R. What is Ixx, Iyy, and Izz? b)...
a) Consider a uniformly dense sphere of radius R. What is Ixx, Iyy, and Izz?
b) Consider a thin circular disk of mass M, radius R. What is Ixx, Iyy, and Izz? Assume in this case that the z-axis points perpendicular to the plane of the disk, while x and y are in-plane.
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a) Consider a uniformly dense sphere of radius R. What is
Ixx, Iyy, and Izz?
b)...
For the next six problems, consider a uniformly charged disk of radius R. The total charge...
For the next six problems, consider a uniformly charged disk of radius R. The total charge on the disk is Q. To find the electric potential and field at a point P (x>0) on the x-axis which is perpendicular to the disk with the origin at the center of the disk, it is necessary to consider the contribution from an infinitesimally thin ring of radius a and width da on the disk, as shown. What is the surface charge density...
Problem 3 (25 points): Magnetic Field from Superposition. A circular disk of radius ro is uniformly...
Problem 3 (25 points): Magnetic Field from Superposition. A circular disk of radius ro is uniformly coated with charge with a surface charge density of ps the disk lies in the x-y plane and the disk axis is the z-axis. This disk is spinning about the z-axis at a rate of one revolution every T seconds. The resulting surface current density on the disk is given by 2Tps a) What is the magnetic field intensity on the z-axis at a...
A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure...
A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure below). Let the rotational inertia of the sphere be Isphere. A massless cord passes around the equator of the sphere, over a pulley with rotational inertia I pulley and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle and the cord does not slip on the pulley. At t = 0, the mass...
help A,B and C..thx 2. A disk of radius R is uniformly charged with total charge...
help A,B and C..thx
2. A disk of radius R is uniformly charged with total charge Q. A. Find an expression for an electric field at a point, x, along the axis perpendicular to the disk. B. Verify that the limit x >>R gives the expected result. C. Find an expression for the limit of an infinitely charged plane.
6. Consider a two dimensional mass distribution in the shape of a thin pizza slice: The mass is uniformly distributed a...
6. Consider a two dimensional mass distribution in the shape of a thin pizza slice: The mass is uniformly distributed and the pizza slice has a radius R and total angle o. Basically you can think of this as a slice of a disk of radius R and angle φ。. a) What is the mass per unit area σ in terms of M, R, and φ? b) Calculate the center of mass of the pizza slice. Check that your answer...
1a) An insulating sphere of radius 2.0 m contains +50 μC of electric charge uniformly distributed...
1a) An insulating sphere of radius 2.0 m contains +50 μC of electric charge uniformly distributed throughout the volume of the sphere. i) What is the electric field 1.5 m away from the center of the sphere? ii) What is the volume charge density? iii) What is the electric field 3.0 m away from the center of the sphere? 1b) A potential difference of 6.00 nV is set up across a 5.00 cm length of copper wire that has a...
A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure...
A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure below). Let the rotational inertia of the sphere be A massless cord passes around the equator of the sphere, over a pulley with rotational inertial and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle and the cord does not slip on the pulley. At 1 = 0, the mass m has speed...
11.Consider a hollow thin conducting sphere of radius R = 10 cm, uniformly distributed with a...
11.Consider a hollow thin conducting sphere of radius R = 10 cm, uniformly distributed with a surface charge density of σ = 10-9 coulombs/cm2. a) Find the field at a radius r > 10 cm. Explain the vector orientation of the field and the magnitude. b) Find the field at a radius r < 10 cm inside the sphere. Explain the vector orientation of the field and the magnitude. c) Now consider two concentric conducting spherical shells, each coated with...
Consider a solid sphere of radius R = 0.6 m that is uniformly charged with ρ...
Consider a solid sphere of radius R = 0.6 m that is uniformly charged with ρ = -16 μC/m3. What is the electric potential a distance 2 m from the center of the sphere?
Consider a solid sphere of radius R = 0.8 m that is uniformly charged with ρ...
Consider a solid sphere of radius R = 0.8 m that is uniformly charged with ρ = -10 μC/m3. What is the electric potential a distance 2 m from the center of the sphere?
For the next six problems, consider a uniformly charged disk of radius R. The total charge on the disk is Q. To find the electric potential and field at a point P (x>0) on the x-axis which is perpendicular to the disk with the origin at the center of the disk, it is necessary to consider the contribution from an infinitesimally thin ring of radius a and width da on the disk, as shown. What is the surface charge density...
Problem 3 (25 points): Magnetic Field from Superposition. A circular disk of radius ro is uniformly coated with charge with a surface charge density of ps the disk lies in the x-y plane and the disk axis is the z-axis. This disk is spinning about the z-axis at a rate of one revolution every T seconds. The resulting surface current density on the disk is given by 2Tps a) What is the magnetic field intensity on the z-axis at a...
A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure below). Let the rotational inertia of the sphere be Isphere. A massless cord passes around the equator of the sphere, over a pulley with rotational inertia I pulley and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle and the cord does not slip on the pulley. At t = 0, the mass...
help A,B and C..thx
2. A disk of radius R is uniformly charged with total charge Q. A. Find an expression for an electric field at a point, x, along the axis perpendicular to the disk. B. Verify that the limit x >>R gives the expected result. C. Find an expression for the limit of an infinitely charged plane.
6. Consider a two dimensional mass distribution in the shape of a thin pizza slice: The mass is uniformly distributed and the pizza slice has a radius R and total angle o. Basically you can think of this as a slice of a disk of radius R and angle φ。. a) What is the mass per unit area σ in terms of M, R, and φ? b) Calculate the center of mass of the pizza slice. Check that your answer...
A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure below). Let the rotational inertia of the sphere be A massless cord passes around the equator of the sphere, over a pulley with rotational inertial and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle and the cord does not slip on the pulley. At 1 = 0, the mass m has speed...
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