Question

An infinitely long rod of radius R carries a uniform volume charge density PKS\rho\ (\rho > 0). a) Show how to use Gauss' Law to prove that the electr

Other
ANSWERED
asked 2021-02-08

An infinitely long rod of radius R carries a uniform volume charge density \(\rho\ (\rho > 0)\).
a) Show how to use Gauss' Law to prove that the electric field inside this rod points radially outward and has magnitude.
\(\displaystyle{E}={\frac{{\rho\cdot{r}}}{{{2}\cdot\epsilon_{{0}}}}}\)
b) Integrate the electric field over an appropriate displacement to find the potential difference from the rod's surface to its axis. State explicity which of those two locations is at the higher potential.

Answers (1)

2021-02-09

image
image
b) By integrating the electric field we get the potential. In the above part (a) we get the electric field is
image

0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-03-30
A long, straight, copper wire with a circular cross-sectional area of \(\displaystyle{2.1}{m}{m}^{{2}}\) carries a current of 16 A. The resistivity of the material is \(\displaystyle{2.0}\times{10}^{{-{8}}}\) Om.
a) What is the uniform electric field in the material?
b) If the current is changing at the rate of 4000 A/s, at whatrate is the electric field in the material changing?
c) What is the displacement current density in the material in part (b)?
d) If the current is changing as in part (b), what is the magnitude of the magnetic field 6.0cm from the center of the wire? Note that both the conduction current and the displacement currentshould be included in the calculation of B. Is the contribution from the displacement current significant?
asked 2021-05-20
Assume that a ball of charged particles has a uniformly distributednegative charge density except for a narrow radial tunnel throughits center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton any where along the tunnel or outside the ball. Let \(\displaystyle{F}_{{R}}\) be the magnitude of the electrostatic force on the proton when it islocated at the ball's surface, at radius R. As a multiple ofR, how far from the surface is there a point where the forcemagnitude is 0.44FR if we move the proton(a) away from the ball and (b) into the tunnel?
asked 2021-03-03
a)
b)
Figure shows a nonconducting rod with a uniformly distributed charge +Q. The rod forms a 10/22 of circle with radius R and produces an electric field of magnitude Earc at its center of curvature P. If the arc is collapsed to a point at distance R from P, by what factor is the magnitude of the electric field at P multiplied?
asked 2021-04-22
Nerve cells are long, thin cylinders along which electric disturbances (nerve impulses) travel. The cell membrane if a typical nerve cell consists of an inner and outer wall separated by a distance of \(\displaystyle{0.10}\mu{m}\). The electric field within the cell membrane is \(\displaystyle{7.0}\cdot{10}^{{{5}}}\) N/C. Approximating the cell membrane as a parallel plate capacitor, determine the magnitude of the charge density on the inner and outer cell walls.
...