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- Consider this sphere. How can we prove that the size of the closed surface is independent of the net electric flux?Consider a quarter-circular, very thin, curved rod with a uniform linear charge density, λ, and aradius, r. Derive an equation for the magnitude of the electric field at the point, P, at the centercurvature of the rod, as shown in the figure below. Write the final answer in terms of λ and r, and simplify your answer as much as possible.The figure here shows a Gaussian cube of face area Aimmersed in a uniform electric field that has the positivedirection of the z axis. In terms of E and A, what is the fluxthrough (a) the front face (which is in the xy plane), (b) therear face, (c) the top face, and (d) the whole cube?
- For each of the closed cylinders shown below, select if the electric fluxes through the top, the wall and the bottom are postive (+), negative (-), zero (0) or unknown (?)Discuss the possibility of choosing Gaussian surface other than the sphere.For instance what if you choose the cylindrical surface as a Gaussian surface, is it possible to use Gauss’s law in order to calculate the electric fieldof a charged sphere? Explain your answer in detail.Consider a uniform electric field of E = (a, b, 0) and a disk of radius R What is the flux through the disk if it sits in the yz-plane? What is the flux through the disk if it sits in the xy-plane? What is the maximum flux through the disk as it rotated through all possible orientations?
- What is the net electric flux through the cylinder (a) shown in (Figure 1)? What is the net electric flux through the cylinder (b) shown in (Figure 2)? Express your answer in terms of the variables E, R, and the constant π.In the configuration shown in the picture below, what is the total predicted angle for electric field at point a?Consider the three-dimensional conductor in the figure, that has a hole in the center. The conductor has an excess charge 7.2 μC on it. What is the electric flux (in N⋅m2/C) through the Gaussian surface S1 shown in the figure? Now put a point of charge 27.4 μC inside the cavity of the conductor. What is the flux (in N⋅m2/C) through the Gaussian surface S1? Now consider the Gaussian surface S2. With the charge still inside the cavity, what is the flux (in Nm2/C) through this surface?
- Use GFSA (Given, Find, Solution, and Answer) on the given space below. Encircle your final answer, write it in scientific notation with 2 decimal places (if possible). An cylinder with radius 1 m and length 1.5 m has an infinite line of charge with a linear charge density of 30 C/m. (Make an illustration of the problem) (a) What is the total charge enclosed by the Gaussian cylinder? (b) What is the electric flux through the cylinder due to the infinite line of charge? (c) Calculate the electric field at a point 3 m away from the infinite line of charge.Figure shows six pointcharges that all lie in the same plane. FiveGaussian surfaces – S1, S2, S3, S3, S4 and S5, -each enclose part of this plane, and Fig. 7 showsthe intersection of each surface with the plane.Rank these five surfaces in order of the electricflux through them, from most positive to mostnegative. Show your solution.A disk of radius 0.10 m is oriented with its normal vector n at 30 degrees to a unform electric field E vector of a magnitude of 2.0x10^3 N/C. What is the electric flux through the disk? (Provide the complete details for the Illustrated Diagram - inside the box, Given, Required, Equation, Solution, and Answer)