A system with a V = 0 at ρ = 3rn and If εγ = 4. Find E 100 at ρ = 6rn due to charge distribution pv = 100 pc/m3
Use cylindrical coordinates to find the mass of the solid Q of density ρ.Q={(x, y, z): 0 ≤ z ≤ 9-x-2 y, x²+y² ≤ 25} ρ(x, y, z)=k \sqrt{x²+y²}Use cylindrical coordinates to find the indicated characteristic of the cone shown in the figure.Assume that the density of the cone is ρ(x, y, z)=k \sqrt{x²+y²} and find the moment of inertia about the z-axis.
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for any "nice" scalar function (x,y,z), the Curl of the gradient of (x,y,z) is Zero.. VxVo = 0 Hint: assume the order of differentiation can be switched 3. Find the volume of a sphere of radius R by integrating the infinitesimal volume element of the sphere. 4. Write Maxwell's equations for the case of electro and magneto statics (the fields do not change in time)...
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...
(a) In cylindrical coordinates (2,6,2) the gradient of a scalar function (0, 0, 2) is given by au 1 au au Vy= ap The divergence of a vector function ep + eo + pao ez az v(p, 0, ) = vp (2,0,ze, + vel,0,)e +v:(0,0,z)e, + θυ: az pa where Up, va, and v, are scalar functions, is given by 1 a i due V.v= (pup) + ρθρ' Let f(0, 0, 2) = e sin() + cos(0) (i) Calculate f....
A cylindrical wire has length 60 cm, diameter 9.0 mm, and resistivity 3.0 x 10-4 2m. When the wire is connected across the terminals of a battery, the magnitude of electric field inside the wire is 15 V/m. (a) (b) Calculate the current in the wire and the power dissipated in the wire. Include SI units with each answer. (10 points) In five minutes, how much charge passes through the wire, how many electrons are contained in this amount of...
a volumetric charge density is defined, in cylindrical coordinates for the region 0,005=<p<=0,02 , 0=<phi<=π/2 , 0=<Z<=0,04 Pv = (p^2 -10^(-4))xZxsin(2phi) C/m^3 and Pv=0 for all remaning space find the maximum Pv and the total charge in space
Given the electric field phasor E-E) ρ-le-jkza, in cylindrical coordinates, where 1.4 , show that it represents an electromagnetic wave propagating in free space by using (a) Maxwell's equations, and (b) Helmholtz equation. (c) Find the magnetic field phasor H. 88 8-9 Given the electric field phasor E -(E.a, +jE a)e n free space, determine (a) propagation direction, (b) H, (c) & and (d) polarization state. 1th yeaeo circularly polarized waves. Given the electric field phasor E-E) ρ-le-jkza, in cylindrical...
V=? Use cylindrical coordinates to find the indicated quantity. Volume of the solid bounded above by the sphere x2 + y2 + z2 = 9, below by the plane z = 0, and laterally by the cylinder x2 + y2 = 1.
In free space, consider the volume charge density ρ,-100 μCm3 present throughout the region 5 mm<r<10 mm and pv-0 for 0<r<5 mm. (a) Find the total charge inside the spherical surfacer 10 mm. in spherical coordinates (b) Find D, at r = 10 mm, Dr(10mm) = 2 (c) If there is no charge for r >10 mm, find D, at-50 mm Dr (50 mm)-- 2 47(r)2