A surface charge distribution S = 2 nC/m2 exists on the body of an infinite cylinder...
A surface charge distribution S = 2 nC/m2 exists on the body of an infinite cylinder of radius 2 m; the z axis is the axis of this cylinder. Surrounding this surface charge distribution is a volumetric charge density V = 4(1 + r) nC/m3 which exists for 3 < r < 4 where r is the cylindrical coordinate in meters. We will attempt to determine the fields produced by these sources using Gauss's Law.
(a) Choose a coordinate system for this problem. Explain your reason for this choice.
(b) What field components should exist here, and what coordinate system variables should they be functions of?
(c) Use Gauss's Law to find the electric field for r < 2 m.
(d) Use Gauss's Law to find the electric field for 2 < r < 3 m.
(e) Use Gauss's Law to find the electric field for 3 < r < 4 m.
(f) Use Gauss's Law to nd the electric field for r > 4 m.
(g) Plot the amplitude of the field for 0 < r < 5 m. Interpret your result.
Homework Answers
Add Answer to:
A surface charge distribution S = 2 nC/m2 exists on the body of
an infinite cylinder...
Problem A.1 - Calculate electric flux f5) The electric field due to an infinite line of...
Problem A.1 - Calculate electric flux f5) The electric field due to an infinite line of charge is perpendicular to the line and has magnitude E . Consider an imaginary cylinder with radius e-25 cm and length L = 40 cm that has an infinite line of positive charge running along its axis. The charge per unit length is 3 HC/m. Do not use Gauss's Law, but actually calculate the flux! a) What is the electric flux through the cylinder...
11. Consider the two infinite, parallel plates below which have uniform surface charge densitics, ni and...
11. Consider the two infinite, parallel plates below which have uniform surface charge densitics, ni and 12 11--9.0 nC/m' and n = + 4.0 nC/m? a) (10 pts) What is the electric field at the midpoint between the two plates, at the position marked by the asterisk in (N/C)? 1811821 Not a point charge r *1811182) 12+(9.08709Nm?) (-2.000 /mn? |(4.0nc !m) T+213.24x10" r. 5.69x105NIC -9.00m² +4. On / m² b) (5 pts) What is the direction of the electric field...
To practice Problem-Solving Strategy 22.1: Gauss's Law. An infinite cylindrical rod has a uniform volume charge...
To practice Problem-Solving Strategy 22.1: Gauss's Law. An infinite cylindrical rod has a uniform volume charge density ρ (where ρ>0). The cross section of the rod has radius r0. Find the magnitude of the electric field E at a distance r from the axis of the rod. Assume that r<r0. a) Find the magnitude E of the electric field at a distance r from the axis of the cylinder for r>r0. Express your answer in terms of some or all...
A uniform electric field is produced due to the charge distribution inside the closed cylindrical surface...
A uniform electric field is produced due to the charge distribution inside the closed cylindrical surface (a) What type of charge distribution is inside the surface? C a positive line charge situated on and parallel to the axis of the cylinder O a negatively charged plane parallel to the end faces of the cylinder C a positively charged plane parallel to the end faces of the cylinder a collection of negative point charges arranged in a line at the center...
L(a) A long (L>> a) cylinder in vacuum has a line charge density p is shown...
L(a) A long (L>> a) cylinder in vacuum has a line charge density p is shown below, (). State the Gauss's law for electric field in words. [1) (i). In order to calculate the electric field inside the cylinder using Gauss's Law, draw an appropriate Gaussian surface in the cylinder. [1] (i). Use the above information or otherwise, show that the electric field in the radial direction Pt inside the cylinder is ,2a (assume that the charge is evenly distributed...
I. (10) A solid cylinder with a charge per u thin cylindrical shell with a charge per unit length...
I. (10) A solid cylinder with a charge per u thin cylindrical shell with a charge per unit length of 2 and a radius of R2. Use Gauss's law to derive the equation for the electric field in the region r < Ri. nit length of 1 and a radius of Ri is surrounded by a 1 |R2
I. (10) A solid cylinder with a charge per u thin cylindrical shell with a charge per unit length of 2 and...
An infinitely long cylindrical conductor with radius R has a uniform surface charge density ơ on...
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)....
mall portion of an infinitely long cylinder is shown. The radius of the cylinder is R...
mall portion of an infinitely long cylinder is shown. The radius of the cylinder is R = 4 m and the charge is uniformly distributed throughout the cylinder with a volume charge density of ρ = 0.6 nC/m^3. Gauss's law to find the magnitude of the electric field at a distance r 18 m from the center of the cylinder as shown. Your answer should be in units of N/C. Use Submit Answer Tries /2
(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) .
An infinite line charge 2 (free charge) passes down the axis of an infissite cylinder of...
An infinite line charge 2 (free charge) passes down the axis of an infissite cylinder of lineas dielectries , of radius Riskside dielektric.com the electric displacement D in all by Find the electric field in all space. u find the betwee belastination in allere d) Find the volume polarisation ( bound) charge for(s) for oss < R. e) Find the surface polarisation charge Test at s=R, f) Jend the electrostatic potential in all space where yoB) = 0
Problem A.1 - Calculate electric flux f5) The electric field due to an infinite line of charge is perpendicular to the line and has magnitude E . Consider an imaginary cylinder with radius e-25 cm and length L = 40 cm that has an infinite line of positive charge running along its axis. The charge per unit length is 3 HC/m. Do not use Gauss's Law, but actually calculate the flux! a) What is the electric flux through the cylinder...
11. Consider the two infinite, parallel plates below which have uniform surface charge densitics, ni and 12 11--9.0 nC/m' and n = + 4.0 nC/m? a) (10 pts) What is the electric field at the midpoint between the two plates, at the position marked by the asterisk in (N/C)? 1811821 Not a point charge r *1811182) 12+(9.08709Nm?) (-2.000 /mn? |(4.0nc !m) T+213.24x10" r. 5.69x105NIC -9.00m² +4. On / m² b) (5 pts) What is the direction of the electric field...
A uniform electric field is produced due to the charge distribution inside the closed cylindrical surface (a) What type of charge distribution is inside the surface? C a positive line charge situated on and parallel to the axis of the cylinder O a negatively charged plane parallel to the end faces of the cylinder C a positively charged plane parallel to the end faces of the cylinder a collection of negative point charges arranged in a line at the center...
L(a) A long (L>> a) cylinder in vacuum has a line charge density p is shown below, (). State the Gauss's law for electric field in words. [1) (i). In order to calculate the electric field inside the cylinder using Gauss's Law, draw an appropriate Gaussian surface in the cylinder. [1] (i). Use the above information or otherwise, show that the electric field in the radial direction Pt inside the cylinder is ,2a (assume that the charge is evenly distributed...
I. (10) A solid cylinder with a charge per u thin cylindrical shell with a charge per unit length of 2 and a radius of R2. Use Gauss's law to derive the equation for the electric field in the region r < Ri. nit length of 1 and a radius of Ri is surrounded by a 1 |R2
I. (10) A solid cylinder with a charge per u thin cylindrical shell with a charge per unit length of 2 and...
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)....
mall portion of an infinitely long cylinder is shown. The radius of the cylinder is R = 4 m and the charge is uniformly distributed throughout the cylinder with a volume charge density of ρ = 0.6 nC/m^3. Gauss's law to find the magnitude of the electric field at a distance r 18 m from the center of the cylinder as shown. Your answer should be in units of N/C. Use Submit Answer Tries /2
An infinite line charge 2 (free charge) passes down the axis of an infissite cylinder of lineas dielectries , of radius Riskside dielektric.com the electric displacement D in all by Find the electric field in all space. u find the betwee belastination in allere d) Find the volume polarisation ( bound) charge for(s) for oss < R. e) Find the surface polarisation charge Test at s=R, f) Jend the electrostatic potential in all space where yoB) = 0
Most questions answered within 3 hours.
-
Of all the different weapons discussed in this chapter that make
up CBRNE,
Which group do...
asked 2 minutes ago -
Draw the molecular orbital diagram for O2-
(oxygen molecule with a negative charge).
asked 5 minutes ago -
Given the following JavaScript code, what will be displayed on
the web page?
var x =...
asked 13 minutes ago -
The cynics, skeptics, epicureans, & stoics were most
philosophies that dealt with:
a. the physical...
asked 15 minutes ago -
The hydronium ion concentration of an aqueous solution of 0.333
M trimethylamine (a weak base with...
asked 16 minutes ago -
A buffer is prepared by partially titrating 50.00 mL of 0.964 M
benzoic acid using 0,100...
asked 19 minutes ago -
For a Generalized Additive Model, what does a large
edf(empirical distribution function) value mean?
Thank you...
asked 32 minutes ago -
questions for Biology lab
An agarose gel electrophoresis assay performed with high quality
will NOT have...
asked 36 minutes ago -
A spring with spring constant 400 N/m is anchored at the bottom
of a frictionless 30^∘...
asked 40 minutes ago -
The half-life of 238U is 4.5×109 yr.
Find the number of disintegrations per hour emitted by...
asked 49 minutes ago -
y[n] = x[n] - 3x[n - 1] + 4x[n - 2]
What is the transfer function...
asked 55 minutes ago -
Which one of the following statements is TRUE?
a.
An agency relationship is when someone hires...
asked 1 hour ago