Imagine a squat cylinder of length L and radius L/4. We want to know the electric...
Imagine a squat cylinder of length L and radius L/4. We want to know the electric field a distance 2L from its center, along the axis of symmetry. Describe step-by-step how you would find the field.
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Imagine a squat cylinder of length L and radius L/4. We want to
know the electric...
A hollow cylinder of radius R and length l has a total charge Q uniformly distributed...
A hollow cylinder of radius R and length l has a total charge Q uniformly distributed over its surface. The axis of the cylinder coincides with the z axis, and the cylinder is centered at the origin. Obtain an expression for the electric potential as a function of z. Sketch a graph of the electric potential as a function of distance z, for -2l < z < 2l.
a) Performing an integral over point-charges (Coulomb's Law) to determine electric field. A cylinder of length...
a) Performing an integral over point-charges (Coulomb's Law) to determine electric field. A cylinder of length Land uniform density p is centered at the origin, with its axis pointing along the 2-direction. Determine the electric field at point X which is a distance a>L/2 from the origin along the z-axis. Please set up the integral carefully-you do not need to evaluate it. z axis b) Which components of the electric field do you expect to be zero? Explain. c) How...
Consider a cylinder of mass M, radius R and length L. (a) Calculate the inertia tensor...
Consider a cylinder of mass M, radius R and length L. (a) Calculate the inertia tensor for rotations about the center of mass in the frame where the z axis is along the axis of the cylinder. Use cylindrical coordinates, where x = r cos θ and y = r sin θ. (b) Find the inertia tensor in the frame where the center of the “bottom side” is at the origin with the z axis along the axis of the...
Consider a uniformly charged cylinder with dimensions of radius r and height h contains a charge...
Consider a uniformly charged cylinder with dimensions of radius r and height h contains a charge in it’s volume. What is the magnitude and direction of the electric field at any point outside the cylinder . Describe each step as you go along .Find the electric field within the cylinder and outside of it. Describe each step as you go along. Consider the total charge Q on a line of length h with the use of Gauss’s law compute the...
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.
(1) Consider a very long uniformly charged cylinder with volume charge density p and radius R...
(1) Consider a very long uniformly charged cylinder with volume charge density p and radius R (we can consider the cylinder as infinitely long). Use Gauss's law to find the electric field produced inside and outside the cylinder. Check that the electric field that you calculate inside and outside the cylinder takes the same value at a distance R from the symmetry axis of the cylinder (on the surface of the cylinder) .
1. A line of charge aligned along the z-axis with a length of L has a...
1. A line of charge aligned along the z-axis with a length of L has a charge density of de(z) = pz Where is the displacement along the axis and 2 = 0 at the center of the line. B gives the linear charge density per length, determining the charge density at a given location of the line. 2=0 - - a. Discuss the meaning of the linear charge density equation and what it physically means about the amount of...
2) A long plastic cylinder with a radius of R and length L has a uniform...
2) A long plastic cylinder with a radius of R and length L has a uniform positive charge density. The total charge on the cylinder is Q. (a) Derive an approximate formula for the electric field as a function of r near the surface at location A. (b) Derive an approximate formula for the electric field as a function of r for locations inside the cylinder near the center such as location B.
A long, cylindrical non-conductor of radius R and length L is placed with it long axis...
A long, cylindrical non-conductor of radius R and length L is placed with it long axis along the Z-axis as shown The cylinder has a total charge Q distributed non-uniformly thrpughout its volume. The charge density is only a function of the radial distance "r" from the cylinder axis and varies as ρ(r):- where α is a constant Vr. 2 +9R2 c) What coordinate system will you use? L (xy,z), (p,o,Z), (,o,)) d) What variables will the magnitude of the...
A right circular cylinder has radius R and length L. and a nonuniform volume charge density...
A right circular cylinder has radius R and length L. and a nonuniform volume charge density p(p). If the z axis is chosen to coincide with the axis of the cylinder, the charge density is p(p) - p{z2) = p(z, z) = .p_0 + beta_ z. This means that the charge density varies linearly along the length of the cylinder. Find the force on a point charge q placed at the center of the cylinder. (Adapted from Reitz. Milford, and...
a) Performing an integral over point-charges (Coulomb's Law) to determine electric field. A cylinder of length Land uniform density p is centered at the origin, with its axis pointing along the 2-direction. Determine the electric field at point X which is a distance a>L/2 from the origin along the z-axis. Please set up the integral carefully-you do not need to evaluate it. z axis b) Which components of the electric field do you expect to be zero? Explain. c) How...
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.
1. A line of charge aligned along the z-axis with a length of L has a charge density of de(z) = pz Where is the displacement along the axis and 2 = 0 at the center of the line. B gives the linear charge density per length, determining the charge density at a given location of the line. 2=0 - - a. Discuss the meaning of the linear charge density equation and what it physically means about the amount of...
2) A long plastic cylinder with a radius of R and length L has a uniform positive charge density. The total charge on the cylinder is Q. (a) Derive an approximate formula for the electric field as a function of r near the surface at location A. (b) Derive an approximate formula for the electric field as a function of r for locations inside the cylinder near the center such as location B.
A long, cylindrical non-conductor of radius R and length L is placed with it long axis along the Z-axis as shown The cylinder has a total charge Q distributed non-uniformly thrpughout its volume. The charge density is only a function of the radial distance "r" from the cylinder axis and varies as ρ(r):- where α is a constant Vr. 2 +9R2 c) What coordinate system will you use? L (xy,z), (p,o,Z), (,o,)) d) What variables will the magnitude of the...
A right circular cylinder has radius R and length L. and a nonuniform volume charge density p(p). If the z axis is chosen to coincide with the axis of the cylinder, the charge density is p(p) - p{z2) = p(z, z) = .p_0 + beta_ z. This means that the charge density varies linearly along the length of the cylinder. Find the force on a point charge q placed at the center of the cylinder. (Adapted from Reitz. Milford, and...
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