Epsilon1=2 Epsilon0 6. In the spherical region #1 (0 r a, 0 θ π ,0 φ...
(10 marks) In class we had a question regarding the spherical coordinate system: Given that rcos θ sin φ y-rsin0 sin o with 0 θ 2π and 0 φ π "Why don't we have 0 θ π and 0 φ 2π instead" (a) (5 marks) Explain why this would not work b) (5 marks) If you really wanted the bounds suggested how could you make it work? (10 marks) In class we had a question regarding the spherical coordinate system:...
what is the electric field at the centre (r-0) of a hemisphere bounded by r-a, 0 < θ 〈 π/2 and 0 < φ 2π, that carries a uniform volumetric charge density ρ,-3φ(구)? (The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) 1.
A disk of radius a in the xy plane carries surface charge of density Ps1 =+ps0/p C/m2 for 0 < φ < π, and ps2 = -Ps0/p C/m2 for π < φ< 2π, where ps0 is a constant. (a) Find the electric field intensity E everywhere on the z axis. (b) Specialize your part a result for distances z >> a.Answer is
Help with question 2 1. what is the electric field at the centre (r = 0) of a hemisphere bounded by r = a, 0 < θ < π/2 and 0 < φ < 2m, that carries a uniform volumetric charge density P3(The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) Consider some charges that are lined up in a straight line. This line of charge carries a uniform linear charge density....
5. Charge distributed on a spherical surface of radius a produces the potential φ(a, 0) φ.cos) on that surface, with θ the polar angle and φ, constant. Expressing answers in terms of the givens only, (a) Find φ(r,0), inside the surface and outside (both charge-free). Use zonal harmonics: Eq (3.65), pg 143. (b) Find the surface-charge density function σ(0). (Recall o-e,AE,ORMAL.) (c) Evaluate the dipole moment of the charge distribution, by comparing your exterior solution in (a) to the standard...
1. what is the electric field at the centre (r = 0) of a hemisphere bounded by r = a, 0 < θ < π/2 and 0 < φ < 2m, that carries a uniform volumetric charge density P3(The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) Consider some charges that are lined up in a straight line. This line of charge carries a uniform linear charge density. Let's make Pl =...
(3) Let a > 0. In spherical coordinates, a surface is defined by r = 2a cos φ for 0 Find the volume of the solid enclosed by the surface, as a function of a. φ S (3) Let a > 0. In spherical coordinates, a surface is defined by r = 2a cos φ for 0 Find the volume of the solid enclosed by the surface, as a function of a. φ S
The magnetic field intensity in all of space is given in terms of spherical coordinates: (1 point) The magnetic field intensity in all of space is given in terms of spherical coordinates: A/m. sin θ Use this knowledge in both parts below. (a) Find the current density (in spherical coordinates) at the point P, whose Cartesian coordinates are (z,ys) = (85,-15,-2). ANSWER: At P, J a+ ag+ ap A/m2 (b) Find the net current, I,flowing through the conical surface S...
Coordinate system in rotation. Consider the Minkowski space in spherical coordinates (t, r, θ, φ) and perform a coordinate transformation to a rotational system given by t '= t, r' = r, θ '= θ, φ' = φ + ωt. (a) Find the metric in the new coordinates and all the Christoffel symbols. (b) Take θ' = θ = π/2. Write the equations of the geodesic and compare with the equations d²xi'/ dt'² = f^i, find the value of the...
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z) and (p',p',z'), and Cartesian coordinates (x, y, z) and (x',y',z'), respectively. Write r - r in all three coordinate systems. Hint: Use Equation 1.2) with a r r and r and r' written in terms of appropriate unit vectors.