Solved Exercise/Numericals - Gauss's Law - Application.
Q.1 A point charge of 30 nC is located at the origin while plane y = 3 carries charge 10 nC / m 2 . Find D at (0, 4, 3)? Ans: Electric flux density (D) at point (0, 4, 3) due to a point charge and line charge is given as: D = D Q + D ρ = 0.019 (0, 4, 3) + 5a y = 0.76 a y + 0.057 a z + 5a y = 5.076 a y + 0.057 a z Q.2 A charge distribution in free space has ρ v = 2r nC / m 3 for 0 < r < 10 m and zero otherwise. Determine E at r = 2m and r = 12m? Ans: Gauss’s law states that: For 0 ≤ r ≤ 10 D r (4πr 2 ) = ∫ ∫ ∫ 2r (r 2 sinθ dr dθ dφ) D r (4πr 2 ) = 4π (2r 4 ) / 4 For r ≥ 10 D r (4πr 2 ) = ∫ ∫ ∫ 2r o (r 2 sinθ dr dθ dφ) D r (4πr 2 ) = 4π (2r o 4 ) / 4 D r (4πr 2 ) = 2πr o 4 Q.3 If D = (2y 2 + z)a x + 4xy a y + x a z C/m 2 , find a) Volume charge density at (-1, 0, 3) b) The flux through the cube defined by 0 ≤ x ≤ 1, c) The total charge enclosed by the cube. Ans: a)...