A cylindrically symmetric charge distribution has a volume charge density that depends on the radial position, r, as follows: rho(r) = rho0(1-r/a) where rho0 is the charge density at the central axis and "a" is just a size constant.
What is the electric field at r = 2a? (For direction, “+” means radially outward and “-” means radially inward.)
A cylindrically symmetric charge distribution has a volume charge density that depends on the radial position,...
The charge distribution described in this problem is
cylindrically symmetric because it is symmetric under the
following three geometric transformations: a translation parallel
to the rod's axis, a rotation by any angle about the rod's axis,
and a reflection in any plane containing or perpendicular to the
rod's axis. In other words, no noticeable or measurable change
occurs if you shift the infinitely-long rod by any distance along
its axis, or turn the rod by any angle about its axis,...
4 A spherically symmetric charge distribution has the following radial dependence for the volume charge density ρ: 0 if r R where γ is a constant a) What units must the constant γ have? b) Find the total charge contained in the sphere of radius R centered at the origin c) Use the integral form of Gauss's law to determine the electric field in the region r R. (Hint: if the charge distribution is spherically symmetric, what can you say...
(a) A solid sphere, made of an insulating material, has a volume charge density of p , where r is the radius from the center of the sphere, a is constant, and a >0. What is the electric field within the sphere as a function of the radius r? Note: The volume element dv for a spherical shell of radius r and thickness dr is equal to 4tr2dr. (Use the following as necessary: a, r, and co.) magnitude E direction...
A sphere of radius R has total charge Q. The volume charge
density (C/m^{3}) within the sphere
is \(\rho=\rho_{0}(1-(r^{2}/R^{2}))\)
This charge desity decreases quadratically
from \(\rho_{0}\)
b) Show that the electric field inside the sphere points
radially outward with
magnitude
c) Show that your results of part (b) has the expected value at
r=R.
Only part f) please!
4 A spherically symmetric charge distribution has the following radial dependence for the volume charge density ρ ρ(r) If r > R where y is a constant a) What units must the constant y have? b) Find the total charge contained in the sphere of radius R centered at the origin c) Use the integral form of Gauss's law to determine the electric field in the region r < R. Hint: if the charge distribution is...
4. A spherically sym metric charge distribution has the following radial dependence for the volume charge density ρ 0 if r > R where γ is a constant a) What units must the constant y have? b) Find the total charge contained in the sphere of radius R centered at the origin. c) Use the integral form of Gauss's law to determine the electric field in the region r < R. (Hint: if the charge distribution is spherically symmetric, what...
A long non conducting cylinder has a charge density p=ar where
a = 4.96 C/m^4 and r is in meters. Concentric around it is a
hollow
This is part of the previous page. I need help with 26, 28,
29.
12 cm 11.7 em 16.7 cm Find the total electrie flux through a spbere centered at the point charge and having radius vacuum is 88S42 × 10-12C/N·m" What is the electric field at 2 cm from theRSa The value of...
An infinitely long cylindrical conductor with radius R has a uniform surface charge density ơ on its surface. From symmetry, we know that the electric field is pointing radially outward: E-EO)r. where r is the distance to the central axis of the cylinder, and f is the unit vector pointing radially outward from the central axis of the cylinder. 3. (10 points) (10 points) (a) Apply Gauss's law to find E(r) (b) Show that at r-R+ δ with δ σ/a)....
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...
A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−r/R) for r≤R ρ(r)=0 for r≥R where ρ0=3Q/πR3 is a positive constant. Part A Find the total charge contained in the charge distribution. Express your answer in terms of some or all of the variables r, R, Q, and appropriate constants. Part B Obtain an expression for the electric field in the region r≥R. Express your answer in terms of some or all of...