6. The electric potential at the surface of a sphere of radius R is constant, i.e.,...
(16 pts total) The potential at the surface of a sphere of radius R is given by Vo k(35cos 0-30cos +5cos+3) where k is a constant. Assume there is no charge inside or outside the sphere. 2. a. (5 pts) Write Vo in terms of Legendre polynomials b. (6 pts) Determine the boundary conditions and find the potential inside and outside the sphere. (5 pts) Find the surface charge density σ(θ) at the surface of the sphere. C.
Consider a charged sphere of radius R. The charge density is not constant. Rather, it blows up at the center of the sphere, but falls away exponentially fast away from the center, p(r)=(C/r2)e-kr where C is an unkown constant, and k determines how fast the charge density falls off. The total charge on the sphere is Q. a) Write down the Electric Field outside the sphere, where r ≥ R, in term of the total Q. b) Show that C=...
5. A hollow sphere of radius R has a potential on the surface of V(θ, d) Vo cos θ. There is no a) Find the potential everywhere inside and outside the sphere. b) Find the electric field everywhere inside the sphere. (You will find it easier to convert the potential to Cartesian coordinates and then find the field.) c) Find the charge density σ(0) on the surface of the sphere using Gauss' law. charge inside or outside the sphere.
Problem 1: A grounded metal sphere with radius R is located at the center of a linear dielectric sphere with radius 2R. The dielectric has a relative permittivity of &r. The composite sphere is exposed to some external fields, which create a potential V-α cosa where α is a constant Find the electric field and the electric displacement in the dielectric, i.e. R<rc2R. Hint: Use the appropriate boundary (surface) conditions to solve for the potential in that region in terms...
There is a conducting sphere of radius R, and electric potential VR. An infinite distance away, V infinity = 0. Show that the sphere's surface charge density is given by
\((30\) marks) The electric potential in \(V(r, \theta)\); mtside a hollow empty sphere of radius 1 satisfies the Laplace equation. On the surface of the sphere, \(V(1, \theta)=1-\cos 2 \theta\). Given that \(\lim _{r \rightarrow \infty} V(r, \theta)=0\), find \(V(r, \theta) .\)
Charge is spread uniformly over the surface of a sphere of radius R. The potential at the sphere's center is V. Find an expression for the net charge Q on the sphere. Express your answer in terms of the variables R, V, and the Coulomb's constant k.
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...
1) (a) A conducting sphere of radius R has total charge Q, which is distributed uniformly on its surface. Using Gauss's law, find the electric field at a point outside the sphere at a distance r from its center, i.e. with r > R, and also at a point inside the sphere, i.e. with r < R. (b) A charged rod with length L lies along the z-axis from x= 0 to x = L and has linear charge density λ(x)...
2. (30 POINTS) A spherical shell of radius R holds a potential on its surface of: V(R, 0) = V.(1 + 2cose - cos20) (a.) Find the potential inside and outside the sphere. (b.) Find the surface charge density on the sphere. (c.) Find the dipole moment and the dipole term of the electric field, Epip.