Solved Exercise/Numericals - Electric Potential, Potential Gradient & Electric Dipole.
Q.1 Determine the electric field due to the following potential: a) V = x 2 + 2y 2 + 4z 2 Ans: = - (2x a x + 4y a y + 8z a z ) = -2x a x - 4y a y - 8z a z V/m b) V = ρ 2 (z + 1) sinφ = - [ 2ρ (z + 1)sinφ a ρ + ρ(z + 1) cosφ a φ + ρ 2 sinφ a z ] = - 2ρ (z + 1)sinφ a ρ - ρ(z + 1) cosφ a φ - ρ 2 sinφ a z Q.2 A point charge of 5 nC is located at the origin. If V = 2v at (0, 6, -8), find a) The potential at A (-3, 2, 6) b) The potential at B (1, 5, 7) c) The potential difference V AB Ans: If V (0, 6, -8) = 2 V In this case x = 0; y = 6; z = -8 Using the scalar relationship between Cartesian and spherical system , we have r = (x 2 + y 2 +z 2 ) 1/2 = (100) 1/2 =10 Hence Electric potential at point r due to a point charge Q located at origin → C = - 2.5 a) Electric potential at point r due to a point charge Q located at a point (-3, 2, 6) is given as: = 3. 929 V b) Electric potential at point r due t...