(a) A sphere with
radius R rotates with constant angular velocity . A
uniform charge distribution is fixed on the surface. The total
charge is q. Calculate the current density
in this scenario where
. Show how the E-field is calculated using Gauss' Law and the
direction (in spherical coordinates) of the current density.
Homework Answers
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(a) A sphere with
radius R rotates with constant angular velocity . A
uniform charge distribution...
Consider a sphere of radius a with a uniform charge distribution over its volume, and a...
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...
A hollow sphere of radius a has uniform surface charge density σ and is centered at...
A hollow sphere of radius a has uniform
surface charge density σ and is centered at the origin. It
sits inside a bigger sphere, also centered at the origin, with
radius b > a and uniform
surface charge density −σ. Because of the spherical
symmetry, the electric field will have the form () =
E(r) r̂, where
negative E(r) corresponds to an
electric field pointing towards the origin, and positive
E(r) corresponds to a field
pointing away. What is E(r)...
A sphere with radius R has charge distribution as given (r,)=k*cos() . Calculate electric dipole moment.(Hint:remember...
A sphere with radius R has charge distribution as given
(r,)=k*cos()
.
Calculate electric dipole moment.(Hint:remember symmetry of charge
distribution)
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Figure 27.33 shows a charge (+ q) on a uniform conducting hollow sphere of radius a...
Figure 27.33 shows a charge (+ q) on a uniform conducting hollow sphere of radius a and placed at the center of a conducting spherical shell of inner radius b and outer radius c. The outer spherical shell carries a charge (- q). What is the charge on the outer surface (c) of the shell. Use Gauss' law to find E(r) at positions: within the conducting spherical (r < a); between the sphere and the shell (a<r< b); inside the...
2. A sphere of radius R has the diclectric constant e. The net charge on the...
2. A sphere of radius R has the diclectric constant e. The net charge on the sphere is zero but it has the polarization P-krf (C/n2) in spherical coordinates (k is a constant with the appropriate units) a) (12 points) Calculate the bound charge density ps(C/m3) and the surface bound charge density ơs(C/m2). b) (15 points) Calculate the E-field for R and for R. Use Coulomb's law with the net bound charge density (volume and surface) as oded. Which component(s)...
The figure shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge...
The figure shows two nonconducting spherical shells fixed in
place. Shell 1 has uniform surface charge density +5.4 C/m2 on
its outer surface and radius 4.0 cm; shell 2 has uniform surface
charge density +3.0 C/m2 on
its outer surface and radius 2.4 cm; the shell centers are
separated by L = 11.7 cm. What is the x-component (with sign) of
the net electric field at x = 2.4 cm?
We were unable to transcribe this imageWe were unable to...
2. A sphere of radius R has the dielectric constant e. The net charge on the...
2. A sphere of radius R has the dielectric constant e. The net charge on the sphere is zero but it has the polarization kr (C/m2) in spherical coordinates (k is a constant with the appropriate units). a) (12 points) Calculate the bound charge density pb (C/m3) and the surface bound charge density ơb (C/m2). b) (15 points) Calculate the E-field for rR and for r>R. Use Coulomb's law with the net bound charge density (volume and surface) as needed....
In the figure the sphere of radius R is solid and non-conductive and has a uniform...
In the figure the sphere of radius R is solid and non-conductive and has a uniform charge volumetric distribution p0. A spherical shell with inner radius 2R and outer radius 3R is concentric with the sphere and unloaded. Find, in terms of p0 and R: a) the value of the electric charge in the sphere, b) the magnitude of the electric field at a radial distance r - 2.5R, c) the value of the surface charge density induced in the...
A charge is glued on the cylindrical surface of a long circular cylinder of radius R....
A charge
is glued on the cylindrical surface of a long circular cylinder of
radius R. The cylinder is made of a linear dielectric material of
dielectric constant
.
Find the electric field inside the cylinder and show that this
field is uniform.
If a small metal sphere of radius a (a<< R) gets into the
center of the cylinder, find the total dipole moment of the setup
by all charges: free charge, bound charge, and induced charge,
given the...
A solid, insulating sphere of radius a has a uniform charge density ρ and a total charge Q
Guided Problem 4 -Gauss's LawA solid, insulating sphere of radius a has a uniform charge density ρ and a total charge Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c as shown in the following figure. (a) Find the magnitude of the electric field in the regions: r<a, a<r<b, and r>c. (b) Determine the induced charge per unit area on the inner and outer surfaces of the hollow sphere.Solution scheme:...
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...
A hollow sphere of radius a has uniform
surface charge density σ and is centered at the origin. It
sits inside a bigger sphere, also centered at the origin, with
radius b > a and uniform
surface charge density −σ. Because of the spherical
symmetry, the electric field will have the form () =
E(r) r̂, where
negative E(r) corresponds to an
electric field pointing towards the origin, and positive
E(r) corresponds to a field
pointing away. What is E(r)...
A sphere with radius R has charge distribution as given
(r,)=k*cos()
.
Calculate electric dipole moment.(Hint:remember symmetry of charge
distribution)
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Figure 27.33 shows a charge (+ q) on a uniform conducting hollow sphere of radius a and placed at the center of a conducting spherical shell of inner radius b and outer radius c. The outer spherical shell carries a charge (- q). What is the charge on the outer surface (c) of the shell. Use Gauss' law to find E(r) at positions: within the conducting spherical (r < a); between the sphere and the shell (a<r< b); inside the...
2. A sphere of radius R has the diclectric constant e. The net charge on the sphere is zero but it has the polarization P-krf (C/n2) in spherical coordinates (k is a constant with the appropriate units) a) (12 points) Calculate the bound charge density ps(C/m3) and the surface bound charge density ơs(C/m2). b) (15 points) Calculate the E-field for R and for R. Use Coulomb's law with the net bound charge density (volume and surface) as oded. Which component(s)...
The figure shows two nonconducting spherical shells fixed in
place. Shell 1 has uniform surface charge density +5.4 C/m2 on
its outer surface and radius 4.0 cm; shell 2 has uniform surface
charge density +3.0 C/m2 on
its outer surface and radius 2.4 cm; the shell centers are
separated by L = 11.7 cm. What is the x-component (with sign) of
the net electric field at x = 2.4 cm?
We were unable to transcribe this imageWe were unable to...
2. A sphere of radius R has the dielectric constant e. The net charge on the sphere is zero but it has the polarization kr (C/m2) in spherical coordinates (k is a constant with the appropriate units). a) (12 points) Calculate the bound charge density pb (C/m3) and the surface bound charge density ơb (C/m2). b) (15 points) Calculate the E-field for rR and for r>R. Use Coulomb's law with the net bound charge density (volume and surface) as needed....
In the figure the sphere of radius R is solid and non-conductive and has a uniform charge volumetric distribution p0. A spherical shell with inner radius 2R and outer radius 3R is concentric with the sphere and unloaded. Find, in terms of p0 and R: a) the value of the electric charge in the sphere, b) the magnitude of the electric field at a radial distance r - 2.5R, c) the value of the surface charge density induced in the...
A charge
is glued on the cylindrical surface of a long circular cylinder of
radius R. The cylinder is made of a linear dielectric material of
dielectric constant
.
Find the electric field inside the cylinder and show that this
field is uniform.
If a small metal sphere of radius a (a<< R) gets into the
center of the cylinder, find the total dipole moment of the setup
by all charges: free charge, bound charge, and induced charge,
given the...
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