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3. (45 pts.) A very long uncharged conducting wire of radius a is surrounded by think...
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...
A very long solid non-conducting cylinder of radius R1 is uniformly charged with a charge density p.
A very long solid non-conducting cylinder of radius R1 is uniformly charged with a charge density p. It is surrounded by a concentric cylindrical tube of inner radius R2 and outer radius R3 as shown in the figure below, and it too carries a uniform charge density p. Determine the electric field as a function of the distance r from the center of the cylinders for R.
(Figure 1)An infinitely long conducting cylindrical rod with a positive charge, per unit length is surrounded...
(Figure 1)An infinitely long conducting cylindrical rod with a positive charge, per unit length is surrounded by a conducting cylindrical shell (which is also infinitely long) with a charge per unit length of -21 and radius , as shown in the figure. Part A What is E (r), the radial component of the electric field between the rod and cylindrical shell as a function of the distance from the axis of the cylindrical rod? Express your answer in terms of...
5. (20 points) For many dielectric materials, the relationship between the displacement field D a...
5. (20 points) For many dielectric materials, the relationship between the displacement field D and the electric field E in the material is linear and can be represented simply by th equation D-eE, where ε is the permittivity of the medium. Consider now two long, co- axial cylindrical conducting shells separated by such a dielectric (see the cross-sectional figure below). Let the surface charge density on the inner cylinder with radius a be +o, and assume that the charge is...
A.) We'll start with a very long coaxial cable that has two parts. There's a conducting...
A.) We'll start with a very long coaxial cable that has two parts. There's a conducting cylindrical inner wire of radius a, and a conducting cylindrical sheath around that with radius b. The space in between (a<r<b) is empty. Let the inner conductor have some linear charge density lambda along its length. Derive an expression for the magnitude of the electric field between the inner and outer conductors as a function of r. B.) Consider the same geometry as the...
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...
A conducting sphere of radius a, at potential Vo, is surrounded by a thin concentric spherical...
A conducting sphere of radius a, at potential Vo, is surrounded by a thin concentric spherical shell of radius b, over which someone has glued a surface charge density σ(8)-k cos θ, where k is a constant and θ is the polar spherical coordinate. (a) Find the potential in each region: (i)r > b, and () a<r<b. [5 points] [Hint: start from the general solution of Laplace's equation in spherical coordinates, but allow for different coefficients in the radial part...
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...
An uncharged metal sphere of radius R is placed in an otherwise uniform electric field E...
An uncharged metal sphere of radius R is placed in an otherwise uniform electric field E E0z. Some polarization will be induced because of the electric field, and the induced charges, in turn, will distort the field around the sphere. Find the potential in the region outside the sphere
P3. A long conducting rod of radius a 3.2 mm is surrounded by an equally long.conxial...
P3. A long conducting rod of radius a 3.2 mm is surrounded by an equally long.conxial conduct cylindrical shell of radius b-32 mm. The electric charge on a 5.0 m section of the rod is 4.5 x 10°C and the same length section of the shell carries a charge of 2.0 x 10°C. Fig b-crossectional view Figa - side view a. (2) Calculate the electrie charge on the interior and (ii) exterior surface of the 5.0 m long section of...
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...
A very long solid non-conducting cylinder of radius R1 is uniformly charged with a charge density p. It is surrounded by a concentric cylindrical tube of inner radius R2 and outer radius R3 as shown in the figure below, and it too carries a uniform charge density p. Determine the electric field as a function of the distance r from the center of the cylinders for R.
(Figure 1)An infinitely long conducting cylindrical rod with a positive charge, per unit length is surrounded by a conducting cylindrical shell (which is also infinitely long) with a charge per unit length of -21 and radius , as shown in the figure. Part A What is E (r), the radial component of the electric field between the rod and cylindrical shell as a function of the distance from the axis of the cylindrical rod? Express your answer in terms of...
5. (20 points) For many dielectric materials, the relationship between the displacement field D and the electric field E in the material is linear and can be represented simply by th equation D-eE, where ε is the permittivity of the medium. Consider now two long, co- axial cylindrical conducting shells separated by such a dielectric (see the cross-sectional figure below). Let the surface charge density on the inner cylinder with radius a be +o, and assume that the charge is...
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...
A conducting sphere of radius a, at potential Vo, is surrounded by a thin concentric spherical shell of radius b, over which someone has glued a surface charge density σ(8)-k cos θ, where k is a constant and θ is the polar spherical coordinate. (a) Find the potential in each region: (i)r > b, and () a<r<b. [5 points] [Hint: start from the general solution of Laplace's equation in spherical coordinates, but allow for different coefficients in the radial part...
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...
An uncharged metal sphere of radius R is placed in an otherwise uniform electric field E E0z. Some polarization will be induced because of the electric field, and the induced charges, in turn, will distort the field around the sphere. Find the potential in the region outside the sphere
P3. A long conducting rod of radius a 3.2 mm is surrounded by an equally long.conxial conduct cylindrical shell of radius b-32 mm. The electric charge on a 5.0 m section of the rod is 4.5 x 10°C and the same length section of the shell carries a charge of 2.0 x 10°C. Fig b-crossectional view Figa - side view a. (2) Calculate the electrie charge on the interior and (ii) exterior surface of the 5.0 m long section of...
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