Write down first two approximations
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- function. 2. Consider a semi-infinite line charge located on the +z axis, with a charge per unit length given by: Ao A(z) = { db e exp(-2/a) z≥0 x 0 are constants. Using spherical coordinates, find the electrostatic potential everywhere, assuming Þ(r → ∞) = 0. It is sufficient to express you answer in terms of definite integrals over r.find the potential function f for the field F=3xi+6yj+7zkA dielectric sphere in an external field. Consider a simple dielec- tric with permittivity e, in the form of a uniform spherical ball of radius a. It is placed at the origin in an external electrostatic potential (x, y, z) = bxy (where r, y, z are Cartesian coordinates and b is a constant). Find the elec- trostatic potential o and electric field E everywhere. %3D
- 2. Given the potential field V = 50(x² - y²)V at point P (-4, 1, 5) that is stipulated to lie on a conductor-free space boundary. Find potential V, electric field Ē,electric field intensity D and ps at point P. Write the equation of the conductor surface.The potential of a thin spherical shell of radius R is given as V(R, 0) = 3 cos² 0 + cos 0 - 1. Both inside and outside the sphere, there is empty space with no charge density. The questions on this page are based on this system. What is the linear combination of the two Legendre polynomials that will generate this potential (Denote a Legendre Polynomial as P₁, where I is the index of the polynomial starting from 1 = 0)? O a. 2P₁ + P₂ O b. 2P3 + P₁ O c. Po + P₁ O d. None of the listed answers. O e. 2P₂ + P1₁ Of. P3 + P2 What is the radial part of the potential V(r, 0) inside the spherical shell for the Pi with the lowest l (i.e. the pre-factor of Pi)? O a. r O b. None of the listed options. O c. r/R O d. 2 O e. O f. (r/R)² 1/²