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Problem 4 A long teflon rod (which is a dielectric cylinder) of radius a has a...
6. Spinning Cylinder A cylinder of radius R and infinite length is made of permanently polarized...
6. Spinning Cylinder A cylinder of radius R and infinite length is made of permanently polarized dielectric. The polarization vector P is everywhere proportional to the radial vector r, such that P = ar, where a is a positive constant. The cylinder rotates around its axis with an angular velocity w This is a non-relativistic problem where wR< c. a) Find the electric field E at a radius r both inside and outside the cylinder. b) Find the magnetic field...
33 3 The axis of an infinitely long circular dielectric tube of inner radius ri and...
33
3 The axis of an infinitely long circular dielectric tube of inner radius ri and outer radius r. coincides with the z-axis. A polarization vector P=î3x +ģ4y exits in the dielectric with €= 2.0€. (a) Express P in cylindrical coordinate. (b) Determine the surface and volume charge densities (Ps and on (c) Show that the total bound charge is zero. (d) Find Ē and D inside the dielectric.
Electrostatics problem 2. An infinitely long circular cylinder of radius a and dielectric constant E is...
Electrostatics problem
2. An infinitely long circular cylinder of radius a and dielectric constant E is placed with its axis along the z-axis and is put in an electric field which would have been uniform in the absence of the cylinder, pointing along the x-axis (see figure). Find the total electric field at all points outside and inside the cylinder. Find the bound surface charge density.
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...
Q5. FORCE DUE TO INDUCED POLARIZATION A) Consider a very long (effectively infinite) half-cylinder of radius...
Q5. FORCE DUE TO INDUCED POLARIZATION A) Consider a very long (effectively infinite) half-cylinder of radius r and uniform surface charge density o. What is the magnitude and direction of the electric field at the center of the cylinder? B) Consider now a thin, long straight wire with uniform positive charge per length 2 at the center of a half-cylinder of inner radius a and outer radius b. The half-cylinder is made of a linear dielectric with susceptibility Xe. You...
3) Didn't I just ask this? A long circular cylinder of radius R carries a magnetization...
3) Didn't I just ask this? A long circular cylinder of radius R carries a magnetization M ksp, where k is a constant, s is the distance from the axis, and ф is the azimuthal unit vector. a) Use ф H- dl = hemet to determine the auxiliary field (H field) both inside and outside of the cylinder b) use H = (110)2-M to determine the magnetic field (B-field) both inside and outside of the cylinder
A long cylinder or aluminum or radius R meters is charged so that it has a...
A long cylinder or aluminum or radius R meters is charged so that it has a uniform charge per unit length on its surface or (a) Find the electric fields at distances r (from the center of the cylinder) that lie inside and outside the cylinder. (Enter the radial component of the electric field. Use any variable or symbol stated above along with the following as necessary: inside outside E (b) Plot electric field magnitude as a function of distanoe...
Problem 3: the infinite cylinder An insulating cylinder that is infinitely long has radius R and...
Problem 3: the infinite cylinder An insulating cylinder that is infinitely long has radius R and a charge per unit length of λ. (Hint: because it is an insulator you should assume that the charge is spread uniformly across its entire volume of the cylinder) a) Use Gauss' Law to calculate the electric field at a point outside of the cylinder as a function of r, the radial distance from the center of the cylinder. (r> R) b) Use Gauss'...
possible. 1. A sphere of radius R consists of linear material of dielectric constant x. Embedded...
possible. 1. A sphere of radius R consists of linear material of dielectric constant x. Embedded in the sphere is a free-charge density ρ= k/r, where k is constant and r is the distance from the sphere's center. (a) Show that ker 2REo is the electrie field inside the sphere. (b) The electric field outside the sphere is 26or2 Find the scalar potential at the center of the sphere, taking the zero of potential at infinite radial distance 2. In...
#6) (25 pts total) An infinitely long cylinder of radius R carries a “frozen-in” magnetization parallel...
#6) (25 pts total) An infinitely long cylinder of radius R carries a “frozen-in” magnetization parallel to the axis M = kpa, where k is a constant and pis the distance from the axis. (a) (12 pts) Calculate all the bound currents. (b) (13 pts) Find the magnetic field, B, inside and outside of the cylinder. (This is for cylindrical coordinates where "s" is the same as “p”)
6. Spinning Cylinder A cylinder of radius R and infinite length is made of permanently polarized dielectric. The polarization vector P is everywhere proportional to the radial vector r, such that P = ar, where a is a positive constant. The cylinder rotates around its axis with an angular velocity w This is a non-relativistic problem where wR< c. a) Find the electric field E at a radius r both inside and outside the cylinder. b) Find the magnetic field...
33
3 The axis of an infinitely long circular dielectric tube of inner radius ri and outer radius r. coincides with the z-axis. A polarization vector P=î3x +ģ4y exits in the dielectric with €= 2.0€. (a) Express P in cylindrical coordinate. (b) Determine the surface and volume charge densities (Ps and on (c) Show that the total bound charge is zero. (d) Find Ē and D inside the dielectric.
Electrostatics problem
2. An infinitely long circular cylinder of radius a and dielectric constant E is placed with its axis along the z-axis and is put in an electric field which would have been uniform in the absence of the cylinder, pointing along the x-axis (see figure). Find the total electric field at all points outside and inside the cylinder. Find the bound surface charge density.
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...
Q5. FORCE DUE TO INDUCED POLARIZATION A) Consider a very long (effectively infinite) half-cylinder of radius r and uniform surface charge density o. What is the magnitude and direction of the electric field at the center of the cylinder? B) Consider now a thin, long straight wire with uniform positive charge per length 2 at the center of a half-cylinder of inner radius a and outer radius b. The half-cylinder is made of a linear dielectric with susceptibility Xe. You...
3) Didn't I just ask this? A long circular cylinder of radius R carries a magnetization M ksp, where k is a constant, s is the distance from the axis, and ф is the azimuthal unit vector. a) Use ф H- dl = hemet to determine the auxiliary field (H field) both inside and outside of the cylinder b) use H = (110)2-M to determine the magnetic field (B-field) both inside and outside of the cylinder
A long cylinder or aluminum or radius R meters is charged so that it has a uniform charge per unit length on its surface or (a) Find the electric fields at distances r (from the center of the cylinder) that lie inside and outside the cylinder. (Enter the radial component of the electric field. Use any variable or symbol stated above along with the following as necessary: inside outside E (b) Plot electric field magnitude as a function of distanoe...
Problem 3: the infinite cylinder An insulating cylinder that is infinitely long has radius R and a charge per unit length of λ. (Hint: because it is an insulator you should assume that the charge is spread uniformly across its entire volume of the cylinder) a) Use Gauss' Law to calculate the electric field at a point outside of the cylinder as a function of r, the radial distance from the center of the cylinder. (r> R) b) Use Gauss'...
possible. 1. A sphere of radius R consists of linear material of dielectric constant x. Embedded in the sphere is a free-charge density ρ= k/r, where k is constant and r is the distance from the sphere's center. (a) Show that ker 2REo is the electrie field inside the sphere. (b) The electric field outside the sphere is 26or2 Find the scalar potential at the center of the sphere, taking the zero of potential at infinite radial distance 2. In...
#6) (25 pts total) An infinitely long cylinder of radius R carries a “frozen-in” magnetization parallel to the axis M = kpa, where k is a constant and pis the distance from the axis. (a) (12 pts) Calculate all the bound currents. (b) (13 pts) Find the magnetic field, B, inside and outside of the cylinder. (This is for cylindrical coordinates where "s" is the same as “p”)
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