we know the magnitude of the electric field at a location onthe x axis and at a

Question

we know the magnitude of the electric field at a location onthe x axis and at a location on the y axis, if we are far from thedipole. A) Find V = VB - VA along a lineperpendicular to the axis of a dipole, Do it two ways from thesuperposition of V due to the two charges, and from the intergal ofthe electric field. B) find V = VC-VD along the axisof the dipole. Include the correct sign. Do it two superposition ofV due to the two charges, and from the intergral of the electricfield. C) what is the change in potential energy U in moving anelectron from D to C ? we know the magnitude of the electric field at a location on the x axis and at a location on the y axis, if we are far from the dipole. A) Find DELTAV = VB - VA along a line perpendicular to the axis of a dipole, Do it two ways from the superposition of V due to the two charges, and from the intergal of the electric field. B) find DELTAV = VC-VD along the axis of the dipole. Include the correct sign. Do it two superposition ofV due to the two charges, and from the intergral of the electric field. C) what is the change in potential energy DELTAU in moving an electron from D to C ?

Explanation / Answer

A)the electric potential due to charge +q at B is
V1 = k * (q/(s/2)) = k * (2q/s) k = (1/4o) = 9 * 109Nm2/C2 the electric potential due to charge -q at B is the electric potential due to charge -q at B is V2 = k * (-q/(-s/2)) = k * (2q/s) the total electric potential is V = V1 + V2 = k * (2q/s) + k * (2q/s) =(4kq/s) the coordinates of the charge +q is (0,(s/2)) and thecoordinates of the charge -q is (0,-(s/2)) the coordinates of the point A is (d,0) the electric potential due to charge +q at A is V1 = k * (q/((d - 0)2 + (0 -(s/2))2)1/2) the electric potential due to charge -q at A is V2 = k * (-q/((d - 0)2 + (0 -(-s/2))2)1/2) the total electric potential is V = V1 + V2 = k * (q/((d -0)2 + (0 - (s/2))2)1/2) + k *(-q/((d - 0)2 + (0 -(-s/2))2)1/2) = 0 the elctric field due to the +q charge at point B is E1 = k * (+q/(s/2)2) = k *(4q/s2) the elctric field due to the -q charge at point B is E2 = k * (-q/(-s/2)2) = -k *(4q/s2) the net electric field at point B is E = (Ex2 +Ey2)1/2 ------------(1) the elctric field due to the -q charge at point B is E2 = k * (-q/(-s/2)2) = -k *(4q/s2) the net electric field at point B is E = (Ex2 +Ey2)1/2 ------------(1) Ex = E1x + E2x =E1 * cos1 + E2 *cos2 and Ey = E1y + E2y =E1 * sin1 + E2 *sin2 1 = 2 = 0o or Ex = E1 * cos(0o) +E2 * cos(0o) = E1 +E2 and Ey = E1 * sin(0o) +E2 * sin(0o) = 0 + 0 = 0 from equation (1) we get or E = E1 + E2 or V = E * (s/2) = (E1 + E2) *(s/2) or V = E * (s/2) = (E1 + E2) *(s/2) B)the electric potential due to the +q charge at point Cis V1 = k * (+q/a + (s/2)) = k * (q/(a + (s/2)) the electric potential due to the -q charge at point C is V2 = k * (-q/a - (s/2)) = k * (q/(a -(s/2)) the total electric potential at point C is VC = V1 + V2 = k * (q/(a +(s/2)) + k * (-q/(a - (s/2)) V2 = k * (-q/a - (s/2)) = k * (q/(a -(s/2)) the total electric potential at point C is VC = V1 + V2 = k * (q/(a +(s/2)) + k * (-q/(a - (s/2)) the electric potential due to the +q charge at point Dis V1 = k * (+q/b + (s/2)) = k * (q/(b + (s/2)) the electric potential due to the -q charge at point Dis V2 = k * (-q/b + (s/2)) = -k * (q/(b -(s/2)) the total electric potential at point D is VD = V1 + V2 = k * (q/(b +(s/2)) - k * (q/(b - (s/2)) V = VC - VD = [k * (q/(a + (s/2))+ k * (-q/(a - (s/2))] - [k * (q/(b + (s/2)) - k *(q/(b - (s/2))] C)the change in potential energy U in moving an electronfrom D to C U = q * V q = 1.6 * 10-19 C the electric potential due to the -q charge at point Dis V2 = k * (-q/b + (s/2)) = -k * (q/(b -(s/2)) the total electric potential at point D is VD = V1 + V2 = k * (q/(b +(s/2)) - k * (q/(b - (s/2)) V = VC - VD = [k * (q/(a + (s/2))+ k * (-q/(a - (s/2))] - [k * (q/(b + (s/2)) - k *(q/(b - (s/2))] C)the change in potential energy U in moving an electronfrom D to C U = q * V q = 1.6 * 10-19 C the total electric potential at point D is VD = V1 + V2 = k * (q/(b +(s/2)) - k * (q/(b - (s/2)) V = VC - VD = [k * (q/(a + (s/2))+ k * (-q/(a - (s/2))] - [k * (q/(b + (s/2)) - k *(q/(b - (s/2))] C)the change in potential energy U in moving an electronfrom D to C U = q * V q = 1.6 * 10-19 C

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