Question

and : No charur inside but there are charges outside the closed (TLC) Distinguishing between and : No producing an electric field. A cubie Gaussian surface with a side has two horizontal faces and is in a uniform electrie field of 30 N/C which is directed vertically upward. (1) Find the net electric flux through the cube. (Hint: If there are equal numbers of field lines going into and out of a CLOSED surface, the net flux through the surface is zero Is a cube a closed surface) Cubic Gaussian Surface in a Uniform Electric Field (2) Consider the following conversation between John and Mary: Mary: The uniform electric field lines which the with plates which are effectively infinite in extent." the cube MAY be due to a parallel plate capacitat John: "I agree. Since the charged capacitor plates producing the electric field are outside the cube and there IS NO net charge enclosed in the cube, cu numbers of Geld lines are going in through one face and coming out through the other. Therefore, the net flux through the whole cube is zero Do you agree or disagree? Explain. If you agree on the figure above in (TLC), draw how the parallel plates of the capacitor may be oriented clearly showing the positive and negative plates (3) Find the numerical value of the flux through the top and bottom faces of the cubes using E cos where A is the area of each face and is the angle between E and the area vector. Explain why one of these contributions is positive and the other negative. (4) What is the flux through each of the side faces of the cube? Explain. (5) What is the net flux through the whole cube after you added the contributions from all faces of the cube? Make sure your answer is consistent with question (1) above. (6) Consider the following conversation between John and Mary: John: "The magnitude of the electric field is 50 N/C at point A but zero at point B because the electric field is perpendicular to the area vector at point B." Mary disagree. Since the problem statement says that the field is uniform, it is 50 N/C directed vertically nward at both points A and B. The angle between the field and the area vector matters only for determining the flux through each part of the surface, not for the field at a point on the surface."

Answer 1

Voy 27

for Cube above shown PA :-$E.ds (ore due to fielt limes going out ward) --Pet Arale cose ..tefield is farallel to direction of Surface Avects at 0-0 ni DA = - so Me (@mxam). Coo - - Coo Nk / - 200 N-m/c Simbulny, Pue - So Nex (2m^2m) .co O (tve due to field lina genug = 200 Nusile into the plane) for Scarface B, D Erf , Surface vector is perpendicular to Electric field lines ie cos 90 = 0 , 9 = $€. dA comb = 0 . nel flus through cube = gut $5+ de +98 +de +øp - -200120c + 200 Nmale = 0

Since we have not flux through the Cube is Zein Thear forro we can conclude cute l a closed Surface groce not flux through a closed Surface is zero (2) I agree with both. In this care plates Ado are acting as parallel place capacitors spaced at a distance an (3) The E. flux A defined as number of electric field lines entering through the Surface for surface A (bottom) all electric field lines are entering So they are taken as positive lie. $= tre) while for Surface C, All electric field lines are leaving Condwand go flux through the surface is negative As calculated in perfon 8 = -200 N-myc Pe=0 (4) 40 = 200N-myc Pp0 de, o op=0 be cause angle bw surface & Electric field lines is go adope to get (5) Nel flux is Zero throughout the cube (6) mary's stadement is correct 1