4. A hollow spherical shell has internal radius a and external radius b, and is made of material of uniform density p. Find the gravitational field and the gravitational potential in the three regions 0 < r b by using (1) the Flux Theorem, and (2) Poisson's equation.
Q: 1. Consider the uniform electric field E = (4300 ĵ+ 2800 k) What is its electric flux through a…
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Q: . Find the surface area of that portion of the paraboloid z = 4-x² - y² that is above the xy plane.
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Q: Example 4. Consider an axisymmetric 2D flow with the velocity field kr 2) = k/127². u₂(r, z) = -kz…
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Q: Q2. Transform the vector V = pâp + zâz to Spherical Coordinates. What is the flux of this vector…
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Q: 3 - Given a scalar field T = (x+3)y² sin(2z) and a vector field A= r*yi+ y?(z+5)k, calculate (3) %3D…
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Q: 1. Electric Flux Density 1.1 Given a coaxial cable with solid inner conductor of radius a, an outer…
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Q: a 0+ b
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- Only solve question #2. Question #1 has already been completed and is for reference to question #2.3 Consider a uniform source of particles inside a box with dx=8 cm , dy=4 cm, and dz=2 cm, centered on the origin. Use hand calculation to model each of the sources (3D, 2D-rectangular x-y, 1D linear x, point at origin) and compare the total flux at distances of 1, 2, 64, and 256 cm above from the origin (in the z direction).Flux and nonconducting shells. A charged particle is suspended at the center of two concentric spherical shells that are very thin and made of nonconducting material. Figure (a) shows a cross section. Figure (b) gives the net flux through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere. The scale of the vertical axis is set by = 6.0 x 105 N-m²/C. (a) What is the charge of the central particle? What are the net charges of (b) shell A and (c) shell B? (a) B (105 N·m²/C) e -Os r
- What physical phenomenon predominantly contributes to the magentic field of the earth? a. Charged particles from the solar wind that enter the earth's atmosphere b. The ionization of metals in the earth's crust c. Ionization in the earth's atmosphere d. Ion convection in the molten liquid shell that surrounds the earth's solid inner core e. The total amount of ferromagnetic iron, cobalt, and nickel that is present in the earth's crust2. Consider an insulating spherical shell of inner radius a and outer radius b. a. If the shell has a net charge Q uniformly distributed over its volume, find the vector electric field in all regions of space (r b) as a function of r. b. Now assume that the shell has a non-uniform charge density given by r2 p(r) = Po ab What is the net charge of the shell? c. For the charge distribution in part (b), find the vector electric field in all regions of space (r b) as a function of r.1. A very large flat insulating sheet with uniform charge per area n (SI units: C/m²) sits in the y-z plane at x = 0. We want to find the electric field at a point Pa distance x from the sheet. Assume P is far from the edges and x is small compared to the size of the sheet. Assume that is positive. From symmetry, the electric field must point directly away from the sheet. We choose to draw the Gaussian surface as a cylinder of radius R that extends a distance x on both sides of the sheet. а. Which statement is true regarding the flux through the Gaussian surface? Choose one answer below! The electric flux through all the surfaces is zero. The flux through the endcaps is zero and the flux through the curved section is positive. The flux through the endcaps is zero and the flux through the curved section is negative. R The flux through the curved section is zero. The flux through the right endcaps is positive and through the left endcaps is negative. The flux through the curved section…
- 2. Consider the radially symmetric flux field j = where = xi + yj + zk. (a) Show that the total flux through any closed surface that does not enclose the origin vanishes. (b) Show that the flux through any sphere centered at the origin is independent of the sphere radius.c) For the same cylindrical shell as in the previous problem, draw and label a Gaussian surface and use Gauss's Law to find the radial electric field in the region r > R2. You may take the positive direction as outward. 0 E (r > R2) =9A. A metal sphere of radius R and charge Q is surrounded by concentric metallic spherical shell of inner radius R1 > R, outer R1 > R1 and load Q1 . This system is surrounded by another concentric metallic spherical shell of inner radius R2 > R1, outer R2 > R2 and of load Q2 . Using suitably chosen Gaussian spherical surfaces, find the charge on the spherical surfaces with radii R, R1, R1, R2, R2
- 1. Consider the Yukawa potential V = g²e T/TO T where r = √√x² + y² + z² and is the distance from the origin and ro is a constant. (This potential arises naturally in nuclear physics but we can imagine it being produced by a specific configuration of electric charge) i) Work in a suitable coordinate system and derive the electric field associated with this potential. ii) Compute the flux through a spherical Gaussian surface centred on the origin as a function of r. iii) Use the above result in the limit that r → ∞ to show that the total charge involved is zero.You are an astronaut, living for a long time interval in the International Space Station (ISS). During your off-duty hours, you have run out of books to read and video games to play. So, your mind wanders to your hobby of music. The last book you read discussed Gauss's law, and you get an inspiration. You plan to attach two nonconducting spheres of radius r = 1.50 cm together using a light insulating string of length L and linear mass density μ = 5.00 x 10-3 kg/m, with the string attached at the surface of each sphere. Then, using the electrical system on the ISS, you will be able to electrify each sphere to a charge of Q = 75.0 μC, uniformly spread over the surface of the sphere. The combination will then be allowed to float freely in the ISS. The spheres will repel, creating a tension in the string. When you pluck the string, you wish it to play a perfect middle C, at 262 Hz. Determine the length of the string (in cm) that you need. (Assume the frequency of 262 Hz is the fundamental…Calculate the absolute value of the electric flux for the following situations (In all case provide your answer in N m2/C): a. A constant electric field of magnitude 300 N/C at a 30 degrees angle with respect to the flat rectangular surface shown in the Figure above. b. A uniform electric field E = (70 i + 90 k) N/C through a 4 cm ×5 cm in the x-y plane. c. A uniform electric field E = (−350 i + 350 j + 350 k) N/C through a disk of radius 3 cm in the x-z plane.