The volumetric charge density in a cylinder with a radius of infinite length changes from the...

The volumetric charge density in a cylinder with a radius of infinite length changes from the axis to ?? = ??. Here k is a constant. Find the electric field inside (r <a) and outside (r> a) of the cylinder.

Expert Solution

Manojponduru answered 1 year ago

Consider a cylinder of radius R = 1000 km and, for our purposes here, infinite length....

Consider a cylinder of radius R = 1000 km and, for our purposes here, infinite length. Let it rotate about its axis with an angular velocity of Ω = 0.18◦/s. It completes one revolution every 2000 s. This rotation rate leads to an apparent centrifugal acceleration for objects on the interior surface of Ω2 R equal to 1 g. Imagine several competing teams living on the interior of the cylinder, throwing water balloons at each other. (a) Show that when...

There is uniformly charged hollow cylinder The cylinder has radius R, length L, and total charge...

There is uniformly charged hollow cylinder The cylinder has radius R, length L, and total charge Q. It is centered on the z-axis, with one end at z=−L/2 and the other at z=+L/2.We are interested in finding the electric field generated by the cylinder at a point P located on the z-axis at z=z0. -Consider a thin ring segment of the cylinder, located at height z and having thickness dz. Enter an expression for the charge dQ of the ring?...

A plasma of uniform charge density po= is contained within a cylindrical shape, of infinite length...

A plasma of uniform charge density po= is contained within a cylindrical shape, of infinite length and radius ro. With what speed must a particle of mass m and charge q perpendicularly strike the cylinder in order to bring it to rest at the center of the cylinder?

A long, solid, insulating cylinder of radius R = 6 cm has a uniform charge density...

A long, solid, insulating cylinder of radius R = 6 cm has a uniform charge density of λ = −3 C/m. Find the electric field magnitude everywhere.

A long isolating cylinder with radius R and a charge density ρ(s) = 3λ πR3 (R...

A long isolating cylinder with radius R and a charge density ρ(s) = 3λ πR3 (R − s) for s ≤ R , 0 for s > R , where λ is a fixed positive line charge density (with units C/m) and s denotes the distance from the center of the cylinder. (a) Explain why the electric field is only a function of s. What is the direction of the electric field? (b) Use Gauss’ law to derive the magnitude...

An infinitely long hollow cylinder of radius R is carrying a uniform surface charge density σ...

An infinitely long hollow cylinder of radius R is carrying a uniform surface charge density σ (φ). (a) Determine the general form of the solution of Laplace’s equation for this geometry. (b) Use the boundary condition σ(φ) = σ0cos(φ) to determine the potential inside and outside of the cylinder. (c) Using your answer to part (b), determine the electric field inside and outside of the cylinder.

A solid dielectric cylinder of length L and radius R has a uniform charge per unit...

A solid dielectric cylinder of length L and radius R has a uniform charge per unit volume ρ. Derive a mathematical expression for the electric field E ! at a point on the axis of the cylinder, a distance z above the center of the cylinder, and outside the cylinder, i.e., for z > L/2. {Simplify and express your answer in terms of the given parameters and fundamental constants.

A long, conductive cylinder of radius R1 = 2.45 cm and uniform charge per unit length...

A long, conductive cylinder of radius R1 = 2.45 cm and uniform charge per unit length λ = 302 pC/m is coaxial with a long, cylindrical, non-conducting shell of inner and outer radii R2 = 8.57 cm and R3 = 9.80 cm, respectively. If the cylindrical shell carries a uniform charge density of ρ = 79.8 pC/m^3, find the magnitude of the electric field at the following radial distances from the central axis: 1.74 c.m= _________ N/C 6.25 c.m= __________...

A solid cylinder of radius 1.5 m has a uniform volume charge density of 15 C/m3....

A solid cylinder of radius 1.5 m has a uniform volume charge density of 15 C/m3. Find the magnitude of the electric field at 1.25 m from the axis of the cylinder. a) what will your gaussian surface be? Make a sketch of the solid cylinder and the gaussian surface with their radii b) Write an expression for the total electric flux through the gaussian surface, that is the LHS (Left hand side) of the Gauss' law (this expression may...

Given an infinite sheet of charge occupying the x-y plane such that the charge density is...

Given an infinite sheet of charge occupying the x-y plane such that the charge density is constant and uniform, find the electric field at any point on the z-axis by: A) Using the point charge formula for the electric field directly in cartesian coordinates. B) Using the point charge formula for the electric field directly in cylindrical coordinates. C) Using the point charge formula for potential in cylindrical coordinates and taking the gradient. DO NOT USE GAUSS'S LAW

Question