(b) Without doing calculations, determine the direction of the electric field E at the origin. Briefly justify your answer. [2 points] (c) Find the electric field E at the origin. [14 points] You may find the following integrals useful + C
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Eo z-h/2 The cylinder in the figure has radius a, height h and lies along the z axis with the ori...
Question 1 2 έρ The cylinder in the figure has radius α, height and lies along the z axis with th...
Question 1 2 έρ The cylinder in the figure has radius α, height and lies along the z axis with the origin in the middle. The cylinder is made by a perfect dielectric material and is polarized. The polarization vector is P -Poa with Po > 0 (a) Find the density of all polarization charge distributions that may exist within or on the cylinder. [4 points] (b) Without doing calculations, determine the direction of the electric field E at the...
ery long dielectric cylinder of radius a and dielectric constant er is placed in a field Eo perpendicular to its A v axis. The electric potential inside the cylinder is r in and the electric potentia...
ery long dielectric cylinder of radius a and dielectric constant er is placed in a field Eo perpendicular to its A v axis. The electric potential inside the cylinder is r in and the electric potential outside the cylinder is The electric field inside of the cylinder is and the electric field outside the cylinder is n11 out-_E Find the surface charge density and take the cylinder axis to be the z-axis and take Eo - Eo
ery long dielectric...
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...
2: 2, (30%) A cylinder of radius ro and height, h has induced polarization vector αχ22....
2: 2, (30%) A cylinder of radius ro and height, h has induced polarization vector αχ22. Find induced total polarized charge, Qvp in the volume of the cylinder.
Suppose a thin disk of dielectric with polarization P=Kz 2, radius a, and height h« a...
Suppose a thin disk of dielectric with polarization P=Kz 2, radius a, and height h« a lies parallel to the xy plane with its center at the origin. What is the approximate Ď field in the middle region of the thin disk (i.e. neglect edge effects).
A charged rod of length L lies along the z-axis, centered at the origin It has...
A charged rod of length L lies along the z-axis, centered at the origin It has a charge distribution: lambda(z) [\lambda_0 * z]/L a.) What coordinate system should be used to describe this system? Explain. b.) What is the total charge Q on the rod? c.) Find an equation for the electric field for (x, y, z), use any coordinate system d.)Find an algebraic equation for the electric field at z /2
Problem 4 A long teflon rod (which is a dielectric cylinder) of radius a has a...
Problem 4 A long teflon rod (which is a dielectric cylinder) of radius a has a permanent polarization set in it of P (s, φ, z-ksi where k is a constant, φ is the cylindrical azimuthal angle, and s is the usual cylindrical radius and s is the cylindrical radial unit vector. Neglect the ends of the rod, it can be considered to be infinite. a) Calculate the bound charges ơb and A-(the bound charge on the surface and in...
2) In figure, a top view of a solid conducting cylinder with radius a - 1 em, whose center is at ...
2) In figure, a top view of a solid conducting cylinder with radius a - 1 em, whose center is at the origin of the coordinate system and +z axis is towards out of page. It is concentric with a hollow cylindrical conductor of inner radius b 3 cm and outer radius c 5 cm. Both cylinders have L-5 m lengths which can be assumed to be infinitely long since L > c. The solid cylinder has total net charge...
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.
10 (b) A long straight metal wire of radius a is directed along the z axis and is surrounded by a coaxial metal cylinde...
10 (b) A long straight metal wire of radius a is directed along the z axis and is surrounded by a coaxial metal cylinder of radius b, thus forming a coaxial waveguide. Consider an electromagnetic wave in this waveguide, with the electric field given by where C is a constant, s is the radius-vector in cylindrical coordinates, and w is the angular frequency of the wave (i) Show that on the inner surface of the outer cylinder, the wave satisfies...
Question 1 2 έρ The cylinder in the figure has radius α, height and lies along the z axis with the origin in the middle. The cylinder is made by a perfect dielectric material and is polarized. The polarization vector is P -Poa with Po > 0 (a) Find the density of all polarization charge distributions that may exist within or on the cylinder. [4 points] (b) Without doing calculations, determine the direction of the electric field E at the...
ery long dielectric cylinder of radius a and dielectric constant er is placed in a field Eo perpendicular to its A v axis. The electric potential inside the cylinder is r in and the electric potential outside the cylinder is The electric field inside of the cylinder is and the electric field outside the cylinder is n11 out-_E Find the surface charge density and take the cylinder axis to be the z-axis and take Eo - Eo
ery long dielectric...
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...
2: 2, (30%) A cylinder of radius ro and height, h has induced polarization vector αχ22. Find induced total polarized charge, Qvp in the volume of the cylinder.
Suppose a thin disk of dielectric with polarization P=Kz 2, radius a, and height h« a lies parallel to the xy plane with its center at the origin. What is the approximate Ď field in the middle region of the thin disk (i.e. neglect edge effects).
A charged rod of length L lies along the z-axis, centered at the origin It has a charge distribution: lambda(z) [\lambda_0 * z]/L a.) What coordinate system should be used to describe this system? Explain. b.) What is the total charge Q on the rod? c.) Find an equation for the electric field for (x, y, z), use any coordinate system d.)Find an algebraic equation for the electric field at z /2
Problem 4 A long teflon rod (which is a dielectric cylinder) of radius a has a permanent polarization set in it of P (s, φ, z-ksi where k is a constant, φ is the cylindrical azimuthal angle, and s is the usual cylindrical radius and s is the cylindrical radial unit vector. Neglect the ends of the rod, it can be considered to be infinite. a) Calculate the bound charges ơb and A-(the bound charge on the surface and in...
2) In figure, a top view of a solid conducting cylinder with radius a - 1 em, whose center is at the origin of the coordinate system and +z axis is towards out of page. It is concentric with a hollow cylindrical conductor of inner radius b 3 cm and outer radius c 5 cm. Both cylinders have L-5 m lengths which can be assumed to be infinitely long since L > c. The solid cylinder has total net charge...
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.
10 (b) A long straight metal wire of radius a is directed along the z axis and is surrounded by a coaxial metal cylinder of radius b, thus forming a coaxial waveguide. Consider an electromagnetic wave in this waveguide, with the electric field given by where C is a constant, s is the radius-vector in cylindrical coordinates, and w is the angular frequency of the wave (i) Show that on the inner surface of the outer cylinder, the wave satisfies...
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