Problem Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at xo distance from its center? (Consider that the surface of the plate lies in the yz plane) Solution A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. So for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E- (1/ 24,2) Since, the actual ring (whose charge is dg) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as - (1/ Xx0 2. We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain E - (x0/ 2. Evaluating the integral will lead us to Qxo E = 4 TTEGR? Xo (x3 + R?)-/2 1/2 For the case where in R is extremely bigger than x0. Without other substitutions, the equation above will reduce to E- Q/

Problem Using the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at xo distance from its center? (Consider that the surface of the plate lies in the yz plane) Solution A perfect approach to this is to first obtain the E-field produced by an infinitesimal charge component of the charge Q. There will be several approaches to do this, but the most familiar to us is to obtain a very small shape that could easily represent our circular plane. That shape would be a ring. So for a ring whose charge is q, we recall that the electric field it produces at distance x0 is given by E- (1/ 24,2) Since, the actual ring (whose charge is dg) we will be dealing with is an infinitesimal part of the circular plane, then, its infinitesimal electric field contribution is expressed as - (1/ Xx0 2. We wish to obtain the complete electric field contribution from the above equation, so we integrate it from 0 to R to obtain E - (x0/ 2. Evaluating the integral will lead us to Qxo E = 4 TTEGR? Xo (x3 + R?)-/2 1/2 For the case where in R is extremely bigger than x0. Without other substitutions, the equation above will reduce to E- Q/

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 86AP: Two non-conducting spheres of radii R1 and R2 are uniformly charged with charge densities p1 and p2...

See similar textbooks

Similar questions

A total charge Q is distributed uniformly throughout a spherical volume that is centered at o1 and has a radius R. Without disturbing the charge remaining charge is removed from the spherical volume that is centered at o2 (see below). Show that the electric field everywhere in the empty region is given by E=Qr40R3 where r is the displacement vector directed from o1 to o2 .
The conductor in the preceding figure has an excess charge of 5.0C . If a 2.0C point charge is placed in the cavity, what is the net charge on the surface of the cavity and on the outer surface of the conductor?
Positive charge is distributed with a uniform density along the positive x-axis from r to , along the positive y-axis from r to , and along a 90( arc of a circle of radius r, as shown below. What is the electric field at O?
The infinite slab between the planes defined by z=a/2 and z=a/2 contains a uniform volume charge density p (see below). What is the electric field produced by this charge distribution, both inside and outside the distribution?
The charge per unit length on the thin rod shown below is . What is the electric field at the point P? (Hint: Solve this problem by first considering the electric field dE at P due to a small segment dx of the rod, which contains charge dq=dx . Then find the net field by integrating dE over the length of the rod.)
Consider a uranium nucleus to be sphere of radius R=7.41015 m with a charge of 92e distributed uniformly throughout its volume. (a) is the electric force exerted on an electron when it is 3.01015 m from the center of the nucleus? (b) What is the acceleration of the electron at this point?
Two large copper plates facing each other have charge densities 4.0C/m2 on the surface facing the other plate, and zero in between the plates. Find the electric flux through a 3cm4cm rectangular area between the plates, as shown below, for the following orientations of the area. (a) If the area is parallel to the plates, and (b) if the area is tilted =30 from the parallel direction. Note, this angle can also be =180+30.
An uncharged spherical conductor S of radius R has two spherical cavities A and B of radii a and b, respectively as shown below. Two point charges +qa and +qb are placed at the center of the two cavities by using non-conducting supports. In addition, a point charge +q0 is placed outside at a distance r from the center of the sphere. (a) Draw approximate charge distributions in the metal although metal sphere has no net charge. (b) Draw electric field lines. Draw enough lines to represent all distinctly different places.
Shown below ale two concentric conducting spherical shells of radii R1 and R2 , each of finite thickness much less than either radius. The inner and outer shell carry net charges q1 and q2 , respectively, where both q1 and q2 are positive. What is the electric field for (a) rR1 ; (b) R1rR2 , and (c) rR2 ? (d) What is the net charge on the inner surface of the inner shell, the outer surface of the inner shell, the inner surface of the outer shell, and the outer surface of the outer shell?
A sphere of radius R has a charge distribution given by rho(r)=A√r where A is a constant. What is the divergence of the electric field at the point r=R/2? Hint: What is the differential form of Gauss’ law?
Find the electric field a distance z above the center of a flat circular disk of radius R (See attatched figure) that carries a uniform surface charge σ. What does your formula give in the limit R → ∞? Also check the case z >> R.
Figure 1.52 shows a spherical shell of charge, of radiusa and surface density σ, from which a small circular piece of radius b << ahas been removed. What is the direction and magnitude of the fieldat the midpoint of the aperture? Solve this exercise using the relationship for a force on a small patch.