The density of the charge distribution with spherical symmetry capability is: OSTSR- Por Py = R...
2. A charge distribution with spherical symmetry has density PoR (1) for 0< R< a, and is zero for R spherical variable. Determine a. Here po and a are constants, and R is the (a) (20 points) E everywhere. (b) (20 points) the potential, V, everywhere.
A charge distribution with spherical symmetry has density: rv = ro for o srsr ry = 0 for r>R a) Find the electric field E for r<R and r>R b) Find the electric potential V(r) at r=R c) Find the electric potential V(r) at r = 0 Hint: Integrate the field E found in (a) between Rand infinity, assuming V(r) = 0 at infinity. Then use the result found in (b) to integrate E between r and zero to find...
2) For a spherical charge distribution in the air: po (02 – r2), when r <a p. when r>a lo, (a) Find E and for r>a (b) Find E and for r<a (c) Find the total charge (d) Show that E is maximum when r=0.7454a
G1. What is E for a spherical shell of charge p=0 for r < R1, p = po for R; <r < R2 and • P=0 for r > R2? R2 R1 Po What is the electric field for an infinitely long cylindrical pipe, inner radius Ry, outer radius R, and with p=Ar2 in the pipe wall between R, and R,? R2 R1 For problem G1 what is V in each region of space?
A hollow spherical shell carries charge density 8 in a region a <r<b. where k is a constant. Find the electric field in the three regions (i) r< a (ii a < r< b,iir >b. Use Gauss's Law For the problem above with the charge distribution Find the potential at the center using infinity as your reference point. V(b)-V(a) =-1,E.dl
Problem #4: An infinitely long hollow cylinder has inner radius r = 0.2m and outer radius r = 0.4m has ρ,-23r nCm3 inside the cylinder. U D in the regions r0.2m, 0.2m0.4m and r> 0.4 m. se Gauss s law to find the electric flux density vector
In free space, consider the volume charge density ρ,-100 μCm3 present throughout the region 5 mm<r<10 mm and pv-0 for 0<r<5 mm. (a) Find the total charge inside the spherical surfacer 10 mm. in spherical coordinates (b) Find D, at r = 10 mm, Dr(10mm) = 2 (c) If there is no charge for r >10 mm, find D, at-50 mm Dr (50 mm)-- 2 47(r)2
Consider a spherical shell with radius R and surface charge density: The electric field is given by: if r<R E, 0 if r > R 0 (a) Find the energy stored in the field by: (b) Find the energy stored in the field by: Jall space And compare the result with part (a)
Problem 1 <15 points> Figure shows a volume that conforms to the spherical coordinate system. The volume current density on the top surface is given as J R cos 0+ in0 + pR .Calculate the total current / passing through the top surface (4,00,360°) 4,300,00) You can use an online integral calculator if you need to find the closed form solution of a complex integral. Here is one: http://www.wolframalpha.com/calculators/integral-calculator/ 0,00,00)
37. Which of the following sets are regular and which are not? Give justi fication (a)(anb2m, n 2 0 and m > 0} (b) {a"b" n = 2m) (d) a-1pis prime)