Question

Consider the triangular gaussian block shown. The cross section of the block is an equilateral triangle with sides of length b. The length of the block is L. The block sits a distance a above a infinite sheet of charge with uniform positive charge density σ. (Only a small section of the sheet is shown in the sketch.) The bottom of the block and the sheet are parallel. Find the electric flux through each side of the block (bottom, both top sides, and both ends) in terms of a, b, L, σ, and ǫ0. Use the outward normal for each side when calculating the flux. Find the total flux for the gaussian surface. Is the total what you expect? Why?

Ya?

Answer 1

Electric flux emptyset = E.A Electric field due to the charged sheet E = sigma/alpha epsilon_0 (directed upwards) Case 2 Electric flux at Bottom of the Block At the Bottom side Area A is directed downwards (outward normal) so between E & A is 180^0 so emptyset_1 = E A cos theta Vertical-bar A Vertical-bar = A = Lb = sigma/2 epsilon_0 times Lb times - 1 = -sigma Lb/2 epsilon_0 Case 2: Electric flux at the top sides At the top sides, angle between E & A i 60^0 so emptyset_2 = E A cos theta = sigma/2 epsilon_0 Lb cos 60 = sigma/2 epsilon_0 Lb 1/2 = sigma/4 epsilon_0 Lb Case 3: Electric flux at the both ends At the ends, Angle between E & A i 90^0 so emptyset_3 = E A cos theta = E A cos 90 = 0 The Total flux for the surface will be zero Total flux = emptyset_1 + 2 emptyset_2 + 2 emptyset_3 = -sigma/2 epsilon_0