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) .

E 3 400 N/C 2.0 m 4

## Answer

a) Electric flux through surface 1, negative sign appears due to the fact that direction of electric filed and surface normal are opposite so theta=180^{o}. 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, d) For the slanting surface i.e, surface 4, the length of slanting side, So flux,

a) Electric flux through surface 1, phi_1 = E^rightarrow middot delta s_1^rightarrow = E delta s_1 cos theta = -400 times 2 times 4 = -3200V_m negative sign appears due to the fact that direction of electric filed and surface normal are opposite so theta = 180 degrees. 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 = E delta s cos 90 degrees = 0 d) For the slanting surface i.e, surface 4, the length of slanting side, 2/L = sin 30 L = 4 so flux, phi_4 = 400 times 4^2 cos(90 – 30) = 400 times 4^2 times 0.5 = 3200V_m