Problem Consider a uniform electric field E directed along the + x axis. Find th

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Problem Consider a uniform electric field E directed along the + x axis. Find the net electric flux through the surface of a cube of edges oriented as shown in Figure 24.5. Strategy Evaluate the net flux by summing up the fluxes through each face of the cube. Note that the flux through four of the faces is zero because E is perpendicular to dA on these faces Figure 24.5 A hypothetical surface in the shape of a cube in a uniform electric field parallel to the x axis. The net flux through the surface is zero. Side 4 is the bottom of the cube and side 1 is opposite side 2 Solution The net flux can be evaluated by summing up the fluxes through each face of the cube. First, note that the flux through four of the faces is zero because E is perpendicular to dA on these faces. In particular, the orientation of dA is perpendicular to E for the faces labeled 3 and 4 in Figure 24.5. Therefore, = 90°, so E·dA = E dA cos 90° = 0, The flux through each face parallel to the xy plane is also zero for the same reason. Now consider the faces labeled 1 and 2. The net flux through these faces is given below For face 1, E is constant and inward, whereas dA is outward ( = 180°), so the flux through this face is the following because the area of each face is A = IE-dA = 11 E dA cos 180° =-ES1 dA =-EA =-E12 Likewise, for 2, E is constant and outward and in the same direction as dA ( is the following. 0°), so the flux through this face Hence, the following is the flux over all the faces

Explanation / Answer

a)Flux=E.A=EA cos¤ where ¤ is angle between electric field and area vector.(area vector is perpendicular to surface)

So Flux= EA cos0=EA=6.15*10^5*2.15=13.2225*10^5 web

2) here angle is 90 degrees cos90 is zero

So flux=0

3) Flux= EA Cos(90-63)

= EA cos27=11.78*10^5 web

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