The electric field in terms of spherical coordinates is defined as follows: E = kr'r Here, k is the constant. Obtain the expression for the charge density. (A) 5kɛ,r² (B) 2kɛ,r² (C) 4kɛ,r? (D) kɛ,r²

The electric field in terms of spherical coordinates is defined as follows: E = kr'r Here, k is the constant. Obtain the expression for the charge density. (A) 5kɛ,r² (B) 2kɛ,r² (C) 4kɛ,r? (D) kɛ,r²

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter25: Gauss’s Law

Section: Chapter Questions

Problem 43PQ: The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R),...

See similar textbooks

Related questions

Q: The volumetric charge density of an infinitely long cylinder of radius R is given by p = po.r2. po…

Q: Consider a long cylindrical charge distribution of radius R with a uniform charge density p. Find…

A: Consider a long, cylindrical charge distribution of radius R with a uniform charge density ρ.

Q: An electric field Ē = ax²î exists in a region. Total electric flux through a sphere of radius R…

Q: A cylindrical of radius R with the right side cut af an angle 30°as shown in the figure below is…

Q: A uniform electric field measured over a square surface with side length d = 16.0 cm makes an angle…

A: The expression for the electric flux is given by, ϕE=EAcosθ Here, E is the electric field, A is the…

Q: A solid insulating sphere of radius R has a volume charge density given by p= poexp(-r/a*), where…

A: We know that for a solid sphere with varying charge density is given by:- E= (∫ρ(r)r2dr) × 1/r2εo.…

Q: he electric field at a distance of 0.6 m from the center of an insulated solid sphere with a radius…

Q: For the configuration shown in the figure below, suppose a = 5.00 cm, b = 20.0 cm, and c = 25.0 cm.…

Q: A long coaxial cable is shown in the figure where the radii of the conducting concentric cylinders…

A: Recall Gauss's law ∮E→.dA→=Q/ε0

Q: Figure 2 shows a nonconducting rod with a uniformly distributed charge Q. The rod forms a…

Q: An infinite cylinder of radius R has a charge density given by p(r) = ar³, where r is the…

A: Solution:Consider a small cylinder element having…

Q: A quarter-disc in the first quadrant has a surface charge density given by K cos φ C/m2 . If the…

A: Solution: Given that charge density p = K cos φ C/m2 radius = b field at point P(0,0, -h)

Q: Consider a long, cylindrical charge distribution of radius R with a uniform charge density p. Find…

Q: If the electric flux density is given by D = x²a, + y²z a,y determine the m volume charge density at…

Q: A cylindrical and long charge distribution has been described by the charge density function shown…

Q: The volume charge density of a spherical charge distribution is given by ρ(r)=ρ0e−ar where ρ0 and a…

Q: The electric field intensity in a region is E = 3x2zax + 2xyay - yz2az N/C. Determine the charge…

A: Charge density can be linear, surface, or volume in nature. A linear charge density is defined as…

Q: A concentric hollow insulating spherical shell with inner radius rj=1R and outer radius r2=4.85R has…

Q: A charge distributed over a spherical volume of radius R, where the volumetric charge density at any…

Q: PRACTICE: Consider the setup shown in the figure below, where the arc is a semicircle with radius r.…

Q: Two concentric spherical shells with radius “R1” and “R2” , charge quantity “Q1” and “Q2”…

Q: A uniform volume charge distribution ρv=5 (nC/m3) exists in a sphere that has a radius of a=3 cm.…

Q: A nonuniform, but spherically symmetric, distribution of charge has a charge density P(r) given as…

Q: The charge density of a non-uniformly charged sphere of radius 1.0 m is given as: For rs1.0 m; p(r)=…

A: Given, Charge density,ρ=ρ0(1-4r3) Radius,R=1 m

Q: A shpere of radius R carrries a volume charge density p=pgr, where po is a constant and r is the…

Q: 30N/C Q.2) The directions of the electric fields on the face of the cube are 40N/C shown in figure.…

A: Net flux through the cube = 1 Nm2/c Net charge in cube q = 8.85 × 10 -12 C

Q: The total outward electric flux going from a cube with 0<x<l, 0<y<l, 0szsl metres containing a…

A: The electric flux through a surface = 1ε0 (net charge enclosed by the surface) In natural unit we…

Q: A solid sphere of radius R carries a uniform volume charge density p . The magnitude of electric…

Q: A solid conducting sphere, which has a charge Q1 -71Q and radius ra- 1.7R is placed inside a very…

A: Given: ra=1.7 R, Q1=71Qrb=4.9R, Q2=-5QFinding E at r=6.7R

Q: Consider a long, cylindrical charge distribution of radius R with a uniform charge density ρ. Find…

A: Given Data The radius of the cylinder is R. The uniform charge density is given as ρ. The…

Q: E, = bx? Let the distribution of electric field strength in a certain area of space be y E, = E. = 0…

A: Given,

Q: The charge density of a non-uniformly charged sphere of radius 1.0 m is given as: For rs 1.0 m;…

Q: Consider a long cylindrical charge distribution of radius R with a uniform charge density ρ.…

A: Given Data : The radius of the cylinder is given as R The charge density of the cylinder is given as…

Q: dx P. + + + + + + t + dq Evaluate an expression for the electric field at point P of a uniformly…

A: Here we first find the electric field due to small element after that we integrate to find the…

Q: In the figure shown in E, and E, be magnitude of electric field at A and B due to the hemisphere of…

Q: An electric field of strength 450 N/C is pointing in the positive x-direction. What would be the…

Q: A disk of radius r= 70 cm has a uniform surface charge density o = 93.2 nC. Calculate the electric…

A: The electric field at a perpendicular distance x from the center of a uniformly charged disc of…

Q: The electric field E is maximum at r equals:

A: Answer is 2R/3 .

Q: The volume charge density of a spherical charge distribution is given by ρ(r) = ρ0 e−αr, where ρ0…

A: Flux ∅=qenc∈o=∫E.dA=E4πr2

Q: A charge distribution that is spherically symmetric but not uniform radially produces an electric…

Q: Charge Q is distributed homogeneously over a spherical shell of inner radius Ri and outer radius R2.…

A: Step 1: Let the charge enclosed by the sphere is denoted by Q and assume the gaussian surface is at…

Q: Electric Field Calculations Using Gauss's Law for the insulating sphere of radius R, r >R with the…

A: The radius of insulating sphere = R The point of observation lies outside the sphere. It means…

Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

100%

The electric field in terms of spherical coordinates is defined as follows:
E = kr'r
Here, k is the constant.
Obtain the expression for the charge density.
(A) 5kɛ,r²
(B) 2kɛ,r²
(C) 4kɛ,r?
(D) kɛ,r²

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

An electric field is found to be <3xyz, 2x2/z, x+y+z>. What is the x-component of the electric field vector at position (2, 6, 1)m?
Consider two thin disks, of negligible thickness, of radius R oriented perpendicular to the x axis such that the x axis runs through the center of each disk. The disk centered at x=0 has positive charge density η, and the disk centered at x=a has negative charge density −η, where the charge density is charge per unit area. What is the magnitude E of the electric field at the point on the x axis with x coordinate a/2? Express your answer in terms of η, R, a, and the permittivity of free space ϵ0.
A solid conducting sphere of radius R carries a positive electric charge Q. For what values or r is the electric field, E(r) = 0?
The volume charge density of a sphere of Radius R is directly related to the radius of the sphere as given by the equation p(r) = br where b is a positive integer. What would be expression for the electric field at r = 1/2 R from the center of the sphere?
If we assume that there is an electric field in the form of E=2zk, which of the following gives the total electric flux through the region?
Two concentric spherical shells with radius “R1” and “R2” , charge quantity “Q1” and “Q2” respectively, find the distribution of electric field strength in space , and make the E-r relationship curve.
This equation is of the electric charge of a uniform disk which is charged at point z which is perpendicular to the center of the disk. (z=0 is part of the plane of the disk). R= radius of disk, Q= total charge of disk, k= coulomb's constant. If k=1 units, Q=1 units, R=8 units, what is Edisk, z when z=6 units?
An infinitely long solid insulating cylinder of radius R has a uniform volume charge density of 0.99μC/m3. If the magnitude of the electric field 0.302m from the axis of the cylinder is 3880N/C, what is R, the radius of the cylinder, in meters? Assume that R<0.302m, so the point of observation is exterior to the cylinder.
An electric field of strength 450 N/C is pointing in the positive x-direction. What would be the total flux through a cube box of side 1m if it is sitting on the x-y plan and one side is making an angle of 32 degrees with the y-axis and contains a charge of value 7.5 nC?
Consider a long cylindrical charge distribution of radius R with a uniform charge density ρ. Calculate the magnitude of the electric eld at a distance R/2 from the axis.
Charge is uniformly distributed around a ring of radius R = 2.40 cm, and the resulting electric field magnitude E is measured along the ring’s central axis (perpendicular to the plane of the ring). At what distance from the ring’s center is E maximum?
If a solid insulating sphere of radius 50 cm carries a total charge of 150 µC uniformly distributedthroughout its volume, what is its a) volume charge density? What is the magnitude of the electricfield at b) 10 cm and c) 65 cm from the center of the sphere.