Consider any charge distribution with a charge densityp(f), let v be a spherical region of radius .. Centered at 0, the average electric field E within v has the formula: 1 | E(F)dv = Ēint + Eext .3 where Ent is the average field due to all internal charges v and Eetis the average field due to all external charges v Prove that Eint 1 4TE0 r3 Eext 1 Sv 4TE0 r13 where Pis the electric dipole moment (cycle O) of the internal charge. and V is the region in space. that includes v and P(F)# 0

Consider any charge distribution with a charge densityp(f), let v be a spherical region of radius .. Centered at 0, the average electric field E within v has the formula: 1 | E(F)dv = Ēint + Eext .3 where Ent is the average field due to all internal charges v and Eetis the average field due to all external charges v Prove that Eint 1 4TE0 r3 Eext 1 Sv 4TE0 r13 where Pis the electric dipole moment (cycle O) of the internal charge. and V is the region in space. that includes v and P(F)# 0

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter15: Electric Forces And Electric Fields

Section: Chapter Questions

Problem 50P: A charge of q = 2.00 109 G is spread evenly on a thin metal disk of radius 0.200 m. (a) Calculate...

See similar textbooks

Similar questions

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.
Consider a cylindrical charge distribution of radius R with uniform charge density ρ. Show that the electric field at a distance r from the axis, where r < R is E = ρr 2ε0
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?
Figure 2 shows a nonconducting rod with a uniformly distributed charge Q. The rod forms a half-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?
Consider a hollow sphere of radii h and 3h, interior and exterior respectively. The charge density on the sphere is ρ=ar, C/m3, where a is a positive constant, and r is the distance from the center of the sphere to an arbitrary point inside the sphere. A point charge with charge Q, of magnitude −16πah4 C, is located at the center of the sphere. Find the electric field, Eux, of the distribution, sphere and point charge, at a point (P), on the x-axis, located at a distance of 2h, measured with respect to the center of the sphere. In this case consider that ah2= 4. Use k=9×109, ux unit vector in the x-direction, π=3.14
A plastic rod with a uniform charge - Q is bent in a 120° circular arc ofradius r and is symmetrically placed across an X axis with the origin atthe center of curvature P of the rod If the linear charge density of the rod is 2, write an expression forthe magnitude of the electric field strength dE at P due todq charge element of the rod.
long coaxial cable is made of an inner solid cylindrical rod of radiusa and an outer cylindrical thin shell of radius b. The inner rod carries auniform volume positive charge density pv . The outer shell carries negativecharge with a uniform surface charge density ps, which is of just the rightamount to make the cable as a whole electrically neutral. Find the electricfield E in the regions: a) inside the inner cylinder (r < a), b) between thecylinders (a < r < b) and c) outside the cable (r > b)
The charge per unit length on the thin rod shownbelow is λ . What is the electric field at the point P? (Hint:Solve this problem by first considering the electric fieldd E→ at P due to a small segment dx of the rod, whichcontains charge dq = λdx . Then find the net field byintegrating d E→ over the length of the rod.)
A charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude E = Kr4, directed radially outward from the center of the sphere. Here r is the radial distance from that center, and K is a constant.What is the volume density r of the charge distribution?
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.
A charge of 10 nC is spread uniformly throughout the volume of a sphereof radius 5 cm. What is the magnitude of the electric field at radial distance of (a) 2 cmand (b) 10 cm?
This equation is for the electric field of a uniform ring which is charged and is at point z which is perpendicular to the center of the ring. (it means z=0 is part of the plane in which the ring is in). R=radius of ring, Q= total charge of ring, k= coulomb's constant. If k=1 units, Q=1 units, R=8 units, what is Ering, z when z=6 units?