7. Calculate the divergence over the volume of a sphere of radius 3 in a vector field where =4rsin- cos.(r, with De...
1 For a vector field A zx +xz y yz Verify Divergence theorem over a sphere, with a radius R and center at the origin 1. 3 points 3 points Converthe vector into eylindrical coordinatces 2. 1 For a vector field A zx +xz y yz Verify Divergence theorem over a sphere, with a radius R and center at the origin 1. 3 points 3 points Converthe vector into eylindrical coordinatces 2.
If a charge is located at the center of a spherical volume and the electric flux through the surface of the sphere is Φ, what should be the flux through the surface if the radius of the sphere were tripled? Draw the diagram with a sphere of radius R and the second surface of radius 3R. Draw enough field lines to illustrate the field. Calculate the flux through each surface. What is the relationship of the flux through radius R...
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...
14. (1 pt) Calculate the flux of the vector field = 6r. where ř = (x, y, z), through a sphere of radius 3 centered at the origin, oriented outward. Flux =
515P) Calculate (r is the usual position vector): 7:7, 7(r-), r •7(r) integrate this over a spherical volume radius b centered at origin: convert this to surface and volume integral.
Charge Q is spread uniformly throughout the volume of a sphere of radius R. The flux through a spherical Gaussian surface of radius r < R (concentric with the sphere of charge) in equal to a) Q/element of_0 b) Qr/element of_0 R c) Qr^2/element of_0 R^2 d) Qr^3/element of_0 R^3
4. The area S enclosed by a circle of radius a in spherical geometry (see Ex. 1) is given by the formula s-2m(1-cosa) COS where r is the radius of the sphere. Deduce from this the formula for the area of a sphere of radius r. 4. The area S enclosed by a circle of radius a in spherical geometry (see Ex. 1) is given by the formula s-2m(1-cosa) COS where r is the radius of the sphere. Deduce from...
A sphere of radius R is centered at the origin. A constant magnetic field of magnitude B is in the +k direction. What is the value of the magnetic flux that passes through the hemispherical surface that has z<0? (This is the half of the surface of the sphere in the region z<0.) Define the flux to be positive if it points from the inside of the sphere to the outside. a) 2 B b) -2B c) - TPB d)...
Use the divergence theorem to calculate the flux of the vector field \(\vec{F}(x, y, z)=x^{3} \vec{i}+y^{3} \vec{j}+z^{3} \vec{k}\) out of the closed, outward-oriented surface \(S\) bounding the solid \(x^{2}+y^{2} \leq 16,0 \leq z \leq 3\).
r 37. Singular radial field Consider the radial field (x, y, z) F (x2 + y2 + z2)1/2" a. Evaluate a surface integral to show that SsFonds = 4ta?, where S is the surface of a sphere of radius a centered at the origin. b. Note that the first partial derivatives of the components of F are undefined at the origin, so the Divergence Theorem does not apply directly. Nevertheless, the flux across the sphere as computed in part (a)...