A non-uniformly charged insulating sphere has a volume charge density p that is expressed asp= Brwhere B is a constant, and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for B?Sol.By definition, the volume charge density is expressed infinitesimally asp=where inis the infinitesimal charge andis the infinitesimal volume.So, we hayep = dq/So we can write this asdq = BdVBut,dV =drBy substitution, we get the followingdq = 4BTdrUsing Integration operation and evaluating its limits, the equation, leads toQ =BTRearranging, we getB =/( T

There are three different types of charge densities in general. The charge distributed per unit…

A non-uniformly charged insulating sphere has a volume charge density p that is expressed as p= Br where B is a constant, and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for B? Sol.

A non-uniformly charged insulating sphere has a volume charge density p that is expressed as p= Br where B is a constant, and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for B? Sol.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A non-uniformly charged insulating sphere has a volume charge density p that is expressed as p= Br where B is a constant, and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for B? Sol. By definition, the volume charge density is expressed infinitesimally as p= where in is the infinitesimal charge and is the infinitesimal volume. so, we have p = dq/ So we can write this as dq = B dV %3D But, dV = dr
A circular ring of radius 23.0 cm has a continuous charge distribution of -1.4 C/m. How many excess electrons are on the ring? Write your result as multiplicative of 1018. Your result must contain one figure after the decimal point. Maximum of 3% of error is accepted in your answer. One electron charge is -1.6x10 19 C.
What is the volume charge density if a total charge of 63 nC is distributed uniformly throughout a 2.7 cm radius sphere?
A cylinder of length L=5m has a radius R=2 cm and linear charge density 2=300 µC/m. Although the linear charge density is a constant through the cylinder, the charge density within the cylinder changes with r. Within the cylinder, the charge density of the cylinder varies with radius as a function p( r) =p.r/R. Here R is the radius of the cylinder and R=2 cm and p, is just a constant that you need to determine. b. Find the constant po in terms of R and 2. Then plug in values of R and 1. to find the value for the constant p. c. Assuming that L>>R, use Gauss's law to find out the electric field E inside the cylinder (rR) in terms of 1. and R. d. Based on your result from problem c, find the electric field E at r=1cm and r=4cm.
This is an equation for an radially directed, electric field of a rod that has finite charge and is uniform. r is the distance of the charge in a plane that bisects the rod. L= length of the rod, Q= Total charge of the rod, k=coulomb's constant. if k=1 units, Q=1 units, L=12 units, what is Erod when r=4?
The inner radius shown in the figure 1m, outer radius 2m and charge density 3 µC Consider the surface charge distributed across the disk. Since the medium is empty m2 space, (a) Find the total charge on the disk. (b) 10m above the axis of the load P to the point 2 [µC|lf a load of is placed, find the force that will act on this load. P(0,0,10m) 2m 1m Ps
Density, density, density. (a) A charge -328e is uniformly distributed along a circular arc of radius 6.00 cm, which subtends an angle of 72°. What is the linear charge density along the arc? (b) A charge -328e is uniformly distributed over one face of a circular disk of radius 3.50 cm. What is the surface charge density over that face? (c) A charge -328e is uniformly distributed over the surface of a sphere of radius 2.00 cm. What is the surface charge density over that surface? (d) A charge -328e is uniformly spread through the volume of a sphere of radius 3.30 cm. What is the volume charge density in that sphere? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The electric field at a point in space is definedas the force per unit charge at that point inspace. We can write the electric field E ofa charge q at a distance d from that charge,experienced by a charge Q, asE =FQ= kqd2.The electric field has a direction such that itpoints toward negative charges and away frompositive charges. Suppose your rub a balloonin your hair and it acquires a static charge of−2 × 10−9 C.What is the magnitude of the electric fieldcreated by the balloon at a location 1 m duenorth of the balloon? Coulomb’s constant is9 × 109 N · m2/C2.Answer in units of N/C. You hair acquired an equal amount of positivecharge when you rubbed the balloon on yourhead.What is the strength of the electric fieldcreated by your head at the location of yourfeet, 1.5 meters below?Answer in units of N/C.
= Three uniform charge distributions are present in a region: an infinite sheet of charge, a finite line charge, and a ring of charge. The infinite sheet of charge at (x, -3, z), where x and z spans from negative to positive infinity, has a charge density Ps 5 nC/m². The finite line charge at (0, -1, z), where z ranges from -2 to 2, has a charge density -4 nC/m. Finally, the ring of charge, with a radius of 3m and charge density PL 2 nC/m, is parallel to the xz-plane centered at (0, 4, 0). All coordinates are in meters. Use the value k = 9 x 10⁹ in your solutions and = answers. Question: Determine the magnitude the electric field due to the infinite sheet charge only at (0, 2, 0).
A line of charge of length L = 42 cm with charge Q = 430.0 nAies along the positive Y axis whose one end is at the origin O. A point charge q = 310.0 µClies on point P = (41, 21.0)Here the coordinates are given in centi-meters. a) Find the Electric field at Pdue to the rod. x component of E Give your answer to at least three significance digits. N/C y component of E Give your answer to at least three significance digits. N/C b)Find the charge density of the rod? why is it in C/mbut not in C/m?? Charge density Give your answer to at least three significance digits. C/m
A solid insulating sphere of radius R has a volume charge density p given by p= pexp(-r/a"), where po.a >0 are both constants and r is the distance from the center of the insulator. Which of the following gives the correct expression for the electric fiekd magnitude at a distancer< R inside the insulator? A. E- exp В. Е exp fo 3 c. E = - (-)} D. E = - e(-)} exp E. E= 1-exp
Density, density, density. (a) A charge -361e is uniformly distributed along a circular arc of radius 5.40 cm, which subtends an angle of 41°. What is the linear charge density along the arc? (b) A charge -361e is uniformly distributed over one face of a circular disk of radius 3.50 cm. What is the surface charge density over that face? (c) A charge -361e is uniformly distributed over the surface of a sphere of radius 4.60 cm. What is the surface charge density over that surface? (d) A charge -361e is uniformly spread through the volume of a sphere of radius 3.30 cm. What is the volume charge density in that sphere?