Find the electric flux φ1 through surface 1 shown in (figure 1).

E 3 400 N/C 2.0 m 4 a) Find the electric flux ?1 through surface 1 shown in (Figure 1) . b) Find the electric flux ?2 through surface 2 shown in (Figure 1) . c) Find the electric flux ?3 through surface 3 shown in (Figure 1) . d) Find the electric flux ?4 through surface 4 shown in (Figure 1) . e) Find the electric flux ?5 through surface 5 shown in (Figure 1) .

Answer

a) Electric flux through surface 1, phi_{1}=vec{E}.vec{Delta s_{1}}=EDelta s_{1}, costheta=-400times 2times 4=-3200Vm negative sign appears due to the fact that direction of electric filed and surface normal are opposite so theta=180o. It also implies that flux is going into the system. b, c and e) For surface 2,3 and 5 direction of electric filed and surface normal is perpendicular so, phi_{2}=phi_{3}=phi_{5}=EDelta s ,cos90^{o}=0 d) For the slanting surface i.e, surface 4, the length of slanting side, frac{2}{L}=sin30 L=4 So flux, phi_{4}=400times 4^{2}cos(90-30)=400times 4^{2}times 0.5=3200Vm

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