Question

F - Working with Surfaces 1) Three common sur hree common surfaces are shown in Fig 8.9 1 Fig. 8-9. Discuss with your lab partners what the area vectors for the surfaces look like. Fig. 8-9 Consider figure 8-10, in which the cube is shown in a uniform electric field. 不不不不不不不不, Fig. 8-10 Compare the electric flux passing through the left face of the cube to the electric flux passing through the right face. What is the electric flux passing through each of the other faces? What is the net electric flux passing through the surface? Make sure this agrees with what you found in question 8 of part B. How many area vectors are needed to describe surface (a) in Fig. 8-9? For object c, the magnitude of each area vector was the total surface area divided by the number of area vectors required to describe the surface. For surface a, the magnitude of each area vector must be infinitesimal. Discuss with your lab partners why this must be so.

Answer 1

Vector n Vector n Vector n Vector n Vector n Vector n Vector n Vector n

Sphere - The Area vector for a sphere will be the direction of any radius from Centre of Sphere going outwards Cylinder - 1For cylindrical surface-will have vectors directed outward from centre of the cylindrical surface perpendicular to axis of cylinder for the circular surfaces at top and bottom - vertically upward and vertically downward respectively Cube = The area vector will be outward perpendicular from all 6 square faces 2. Flux passing through left face = Flux Passing through Right Face = Electric flux in all other faces = Net Electric Flux Passing through all surfaces = EA-EA+0-0+0-0 = 0 The number of area vectors for a sphere are infinite- since a perpendicular can be erected at any point on surface of sphere. In the case object c. of Cube or cuboid, the area vector is represented by 1 perpendicular vector per face of the cube, hence magnitude of area vector = A/ no. of area vectors needed = A/1 = A In the case of Object a ,sphere , number of area vectors is infinite, because each of them has different direction hence magnitude of each area vector = area of sphere / infinite number of area vectors = ver small area = Delta (A)