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6. An infinite cylinder of radius R has a uniform charge density of ρ in its...
6. An infinite cylinder of radius R has a uniform charge density of p in its...
6. An infinite cylinder of radius R has a uniform charge density of p in its interior, and a surface charge density of -pR on its surface. Find the electric field everywhere inside and outside the cylinder. Be clear about both the magnitude and direction of the field.
4. An infinite cylinder of radius R has a uniform charge density p except for a...
4. An infinite cylinder of radius R has a uniform charge density p except for a cylindrically shaped cutout of radius R/2, as shown. Find the electric field along the axis of the cylinder. Find the electric potential along the axis of the cylinder, assuming a zero point at some arbitrary distance from the axis of the cylinder. a. b.
Consider an infinitely long straight cylinder of radius R and uniform positive charge density ρ. (a)...
Consider an infinitely long straight cylinder of radius R and uniform positive charge density ρ. (a) Find the field inside the cylinder a distance r < R from the center. (b) Find the field outside the cylinder a distance r > R from the center. (c) Sketch a plot of E vs r over the range 0 ≤ r ≤ 2R.
8. A long coaxial cable (Fig 2b ) carries a uniform volume darge density ρ on...
8. A long coaxial cable (Fig 2b ) carries a uniform volume darge density ρ on the inner cylinder (radius a), and a uniform surface charge density ơ on the outer cylindrical shell (radius b. This surface charge is negative and of just the right magnitude so that the cable as a whole is electrically nt Find the electric field in each of the three regions:) inside the nnr cylinder (s < a), (ii) between the cylinders (a < s...
A solid insulating sphere of radius R has a non-uniform charge density ρ = Ar2 ,...
A solid insulating sphere of radius R has a non-uniform charge density ρ = Ar2 , where A is a constant and r is measured from the center of the sphere. a) Show that the electric field outside the sphere (r > R) is E = AR5 /(5εor 2 ). b) Show that the electric field inside the sphere (r < R) is E = AR3 /(5εo). Hint: The total charge Q on the sphere is found by integrating ρ...
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...
1. A very long, uniformly charged cylinder has radius R and charge density p. Determine the...
1. A very long, uniformly charged cylinder has radius R and charge density \rho. Determine the electric field of this cylinder inside (r<R) and outside (r>R)2. A large, flat, nonconducting surface carries a uniform surface charge density σ. A small circular hole of radius R has been cut in the middle of the sheet. Determine the electric field at a distance z directly above the center of the hole.3. You have a solid, nonconducting sphere that is inside of, and...
Problem 5 Compute the total charge inside in a cylinder of length h and radius Rcy,...
Problem 5 Compute the total charge inside in a cylinder of length h and radius Rcy, when ρ(R) αR. Use the result to compute the electric field produced by the cylinder at points outside the cylinder (rRcyl). Note that since > Rcyl, the Gaussian surface (with radius r) encloses all the charge in the cylinder. State the direction of the electric field inside and outside the cylinder when a > 0, that is, when the cylinder carries positive charge. Problem...
Plaese help! Suppose you have an infinite non-conducting cylinder of charge of radius R, and uniform...
Plaese help!
Suppose you have an infinite non-conducting cylinder of charge of radius R, and uniform charge density lambda. Starting from Gauss' Law, show: that the Electric Field inside is given by: E = lambda r/2 pi epsilon_o R^2 the Electric Field outside is given by E = lambda/2 pi epsilon_o r A big part of your grade will depend on how accurate and detailed your picture is, and how clean and clear your resulting derivation is.
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...
6. An infinite cylinder of radius R has a uniform charge density of p in its interior, and a surface charge density of -pR on its surface. Find the electric field everywhere inside and outside the cylinder. Be clear about both the magnitude and direction of the field.
4. An infinite cylinder of radius R has a uniform charge density p except for a cylindrically shaped cutout of radius R/2, as shown. Find the electric field along the axis of the cylinder. Find the electric potential along the axis of the cylinder, assuming a zero point at some arbitrary distance from the axis of the cylinder. a. b.
8. A long coaxial cable (Fig 2b ) carries a uniform volume darge density ρ on the inner cylinder (radius a), and a uniform surface charge density ơ on the outer cylindrical shell (radius b. This surface charge is negative and of just the right magnitude so that the cable as a whole is electrically nt Find the electric field in each of the three regions:) inside the nnr cylinder (s < a), (ii) between the cylinders (a < s...
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...
Problem 5 Compute the total charge inside in a cylinder of length h and radius Rcy, when ρ(R) αR. Use the result to compute the electric field produced by the cylinder at points outside the cylinder (rRcyl). Note that since > Rcyl, the Gaussian surface (with radius r) encloses all the charge in the cylinder. State the direction of the electric field inside and outside the cylinder when a > 0, that is, when the cylinder carries positive charge. Problem...
Plaese help!
Suppose you have an infinite non-conducting cylinder of charge of radius R, and uniform charge density lambda. Starting from Gauss' Law, show: that the Electric Field inside is given by: E = lambda r/2 pi epsilon_o R^2 the Electric Field outside is given by E = lambda/2 pi epsilon_o r A big part of your grade will depend on how accurate and detailed your picture is, and how clean and clear your resulting derivation is.
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...
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