4. Find the total charge of a solid cylinder of height H and radius R. The...
Find the electric dipole moment of a cylinder of radius R and height h. The volume charge density in the cylinder is given by ρ(z) = k·cos(πz/h). The z-axis is the axis of the cylinder, and the origin is placed at the bottom of the cylinder. Give the answer in terms of k, h, and R in unit vector notation.
A solid cylinder of height L and radius R has uniform mass density . Find the moment of inertia tensor about the center of the cylinder. For what value of L/R is the cylinder equally easy to spin about any axis?
4) A nonconducting sphere of radius Ro and total charge Q, contains a non-uniform volume charge density p -A/r (where A is a constant) throughout the she (a) Find the constant A in terms of Ro, k and Q (b) Find the electric field for r < Ro and r Ro.
Problem 4 (20 points): A long, solid conducting cylinder of radius R has a current density within it described by: (r)-C( ) for r< R where C is a constant to be determined. The total current running through the whole cylinder is I. a) Calculate an expression for the constant C, given that the total current is I. (Hint: the current density is not uniform.) b) Why can Ampere's law be used here, and what Amperian loop is appropriate? c)...
You have long solid cylinder of radius R and charge density p (charge per unit volume). (a) Find electric potential V(r) at distance r < R from the axis of the cylinder. (b) Find electric potential V (r) outside the cylinder at distance r > R. (c) sketch a graph of the electric potential V (r) as a function of r, from r = 0 to r = 4R, with r along the horizontal axis of the graph.
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...
Consider a very long, round, solid nonconductive cylinder of radius R with a volume charge density of rho = -Cr, centered on the z-axis. Where r is the distance from the z-axis, and C is a positive constant. a) What are the units for C? Use Gauss's Law to find the electric field everywhere in space in and around this charged rod, at b) r lessthanorequalto R and c) r > R. This cylinder is long enough that you can...
We have a very long non-conductive solid cylinder with radius R, with a volumetric charge density given by p. Construct in detail an equation to calculate the magnitude of the electric field at a point within the volume of the cylinder at a distance r from its center? What will be the electric field on the surface of the cylinder?
1. A cylinder of mass m, height h and radius r floats partially submerged in a liquid of density ρ. One third of the height of the cylinder is above the surface of the water. Johnny pushes the cylinder down by a small distance x<h/3, then he releases it from rest. A) prove that the resulting motion of the cylinder is a simple harmonic motion. B) Find the period of the small oscillations in terms of the given quantities (m,r,h,ρ)
this is a laplace equation in cylinder coordinates: )
1. (10 points) A solid cylinder of radius a and height h has its curved surface held at 0 °C and its top and base held at a temperature To. Find the steady-state temperature distribution in the cylinder. For your convenience, the PDE and the boundary conditions are given below: lu
1. (10 points) A solid cylinder of radius a and height h has its curved surface held at 0 °C...