A spherical shell of radius a has a uniform surface charge density σ and rotates with...

A spherical shell of radius a has a uniform surface charge density σ and rotates with a constant angular velocity ω in relation to an axis that passes through its center. In this situation, determine the magnetic dipole moment μ of the spherical shell.

Expert Solution

genius_generous answered 1 year ago

Consider a spherical shell with radius R and surface charge density σ. By integrating the electric...

Consider a spherical shell with radius R and surface charge density σ. By integrating the electric field, find the potential outside and inside the shell. You should find that the potential is constant inside the shell. Why?

surface charge density which is σ=σ0 cosθ is distributed on the spherical shell with radius R...

surface charge density which is σ=σ0 cosθ is distributed on the spherical shell with radius R .Using the Laplace eqn find electric potential outside the sphere .

A nonconducting disk has a radius R, carries a uniform surface charge density s, and rotates...

A nonconducting disk has a radius R, carries a uniform surface charge density s, and rotates with angular speed w. (a) Consider an annular strip that has radius ?, width ??, and charge ??. Show that the current produced by this strip is ?? = ?????. (b) Show that the net magnetic field at the center of the disk is ?)???⁄2. (c) Find the magnetic field on the axis of the disk, a distance z from the center.

A spherical shell with radius R and superficial charge density, It rotates around the z-axis through...

A spherical shell with radius R and superficial charge density, It rotates around the z-axis through its center with a constant angular frequency. The magnetic field formed in the center as a result of the rotation of the spherical shell Found it.

An insulated spherical shell of inner radius a1 and outer radius a2 has a charge density...

An insulated spherical shell of inner radius a1 and outer radius a2 has a charge density ρ=6r C/m4. (a) (2 pts.) Based on the symmetry of the situation, describe the Gaussian surface (if any) that could be used to find the electric field inside the spherical shell. (b) (3 pts.) Starting from the definition of charge enclosed, briefly derive the integral expression for the charge enclosed inside a Gaussian surface within the insulated spherical shell for the given charge density....

2. A thin disk of radius R and uniform surface charge density sigma rotates about its...

2. A thin disk of radius R and uniform surface charge density sigma rotates about its axis of symmetry with angular velocity omega = omega zhat. (a) What is the current density K(s) where s is the distance from the center? (b) Find B at the center of the disk (z=0, s=0) using Bio-Savart's law. (It's a simple integral). (c) What is the magnetic dipole moment of the disk?

An infinitely long hollow cylinder of radius R is carrying a uniform surface charge density σ...

An infinitely long hollow cylinder of radius R is carrying a uniform surface charge density σ (φ). (a) Determine the general form of the solution of Laplace’s equation for this geometry. (b) Use the boundary condition σ(φ) = σ0cos(φ) to determine the potential inside and outside of the cylinder. (c) Using your answer to part (b), determine the electric field inside and outside of the cylinder.

a uniform spherical shell of mass M and radius R rotates about a vertical axis on...

a uniform spherical shell of mass M and radius R rotates about a vertical axis on frictionless bearing. A massless cord passes around the equator of the shell, over a pulley of rotational inertia I and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object after it has fallen a distance h from rest?...

A metal sphere of radius a has a uniform (free) charge density σf on its surface....

A metal sphere of radius a has a uniform (free) charge density σf on its surface. The permittivity of the dielectric region surrounding the sphere varies as , where r is the radial coordinate. (1 pts) Determine the polarization P and electric field intensity E inside the sphere. (3 pts) Determine the polarization P and electric field intensity E in the dielectric. (5 pts) Calculate all bound charge densities, ρb and σb. Is the dielectric homogeneous? (1 pts) Test whether...

Consider a spherical charge distribution of radius R with a uniform charge density ρ. Using Gauss'...

Consider a spherical charge distribution of radius R with a uniform charge density ρ. Using Gauss' Law find the electric field at distance r from the axis where r < R.

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