Find the Volume ρ = 1 + 0.2 sen 8Øsen φ 77, 0 2. ρ = 1 + 0.2 sen 8Øsen φ 77, 0 2.
Given the electric potential Φ = 10???? (V) in free space. Find ? ⃗ and ρ? at point P(1, ? = 60°, Φ= 30°)
(b) Find the 2 elements x in Φ(289) such that x2 = 77 (mod 289) (Hint. First solve the congruence modulo 17.)
1) Find the expressions for the unit vectors in cylindrical coordinate system, p, φ,2. in terms of x, ý, 2. Find the time-derivative of each. Hints: Unit vector p is defined in (x, y) plane. Remember that α -φ is perpendicular to a The easiest way to find φ is to express ρ through φ and add 90 degrees
PLE 2 The point (0, 5 3 , −5) is given in rectangular coordinates. Find spherical coordinates for this point. SOLUTION From the distance formula we have ρ = x2 + y2 + z2 = 0 + 75 + 25 = 10 Correct: Your answer is correct. and so these equations give the following. cos(φ) = z ρ = -1/2 Correct: Your answer is correct. φ = $$ Incorrect: Your answer is incorrect. cos(θ) = x ρ sin(φ) = θ...
angular momentum components in cylindrical coordinates Find Mr, My. Mz, M2 in cylindrical coordinates (ρ, φ, z).
(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
1 Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. ญา D is the triangular region with vertices (0, 0), (2, 1), (0, 3); function 2- Use polar coordinates to combine the sum 3- Find the volume of the solid that lies between the paraboloid zxy2 and the sphere x2 + y2+ z22. 1 Find the mass and center of mass of the lamina that occupies the...
Find the solution to ∇2 Ψ(r, θ, φ) = 0 inside a sphere with the following boundary conditions: ∂Ψ (1,θ,φ)=sin2θcosφ.∂r Find the solution to V2(r, e, p) =0 inside a sphere with the following boundary conditions: ay (1, e, p) sin20 cosp. ar Find the solution to V2(r, e, p) =0 inside a sphere with the following boundary conditions: ay (1, e, p) sin20 cosp. ar
1. Find the magnetic field intensity H everywhere in air due to the volume current density J- uniformly distributed over the inner cylinder o radiusa in the region 0spsa,oses 2r.-acz < and the uniform surface current distribution J.-i,, which nows on the cylindrical shell that is located at ρ=b,0 φ 2r,-oczco. Note that both current densities flow in the 2 direction
u(x1, x2) = [x 1^ ρ + x2^ ρ ] ^(1 /ρ) where 0 < ρ < 1 compute the marshallian demand, indirect utility function, the expenditure function and the Hicksian demand function