A charge distribution with spherical symmetry has density: rv = ro for o srsr ry =...
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.
The density of the charge distribution with spherical symmetry capability is: OSTSR- Por Py = R Py = 0, r>Re Find Ē at all point (use gauss law)
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
Calculate the electric potential V at a distance r from an infinite line charge, density rho_t Coulombs per meter. From the potential calculate the electric field and show that the field is identical to what we derived in class You will find that difficulties will arise when integrating from -infinity to infinity to find V. Try this: calculate the potential and the field for a segment of line charge 2L meters long (i.e., integrate from -L to +L). Once the...
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 spherical metal (conductor) has a spherical cavity in side. There is a single point charge Q at the cavity center. The total charge on the meta is 0 (a) Describe how the charge is distributed on the E=? sphere. Would the surface charge density be u form at each surface? (b) Draw the electric field lines. c) Find the electric field for a point outside the metal. Express it in terms of r, the distance of the point in...
A thick-walled spherical shell of charge Q and uniform charge density ρ is bounded by radii r1 and r2 > r1. With V = 0 at infinity, find the electric potential V as a function of distance r from the center of the distribution, considering the three regions: (a) r > r2 (b) r2 > r > r1 (c) r < r1 Finally, comment on whether these solutions agree with each other at r = r1 and r = r2.
A thick spherical shell witn uniform volume charge density ? is bounded by radii r1 and r2 > r1. With V = 0 at infinity, find the electric potential V as a function of distance r from the center of the distribution, considering regions (a) r > r2, (b) r2 > r > r1, and (c) r < r1. (d) Do these solutions agree with each other at r = r2 and r = r1?
2. Potentials and a Conducting Surface The electric potential outside of a solid spherical conductor of radius R is found to be V(r, 9) = -E, cose (--) where E, is a constant and r and 0 are the spherical radial and polar angle coordinates, respectively. This electric potential is due to the charges on the conductor and charges outside of the conductor 1. Find an expression for the electric field inside the spherical conductor. 2. Find an expression for...
A spherical system has electric field E(r) = E(0)exp(-r/R) E(0) and R are constant, r is distance to the center of sohere. Using Gauss law in differential form find electrostatic potential and volume charge density. E. Potential is 0 at infinity. Answer is expected in the form of equation (no numbers required)