Question

Consider the drawings below. All the charges are the same distance from the origin *y 5.0 uC +1.0 uC +2.0 μC 3.0 uC +4.0 HC +X +X +6.0 uC Diagram 1 Diagram 2 a. Without doing any calculations, does the electric field at the origin in diagram 1 have a magnitude that is greater than, less than, or equal to the magnitude of the field at the origin in diagram 2? Justify your answer b. Lets say the distance between the charges and the origin is 6.1 cm. For each diagram shown, determine the magnitude and direction of the electric field at the origin

Answer 1

for diagram 1

net effective horizontal charge = 2 + 3 = 5 uC

net effective vertical charge = 5 uC

for diagram 2

net effective horizontal charge = 4 +1 = 5 uC

net effective vertical charge = 6-1 = 5 uC

so considering all factors (without calculation) the magnitude ( direction as well) of electric field at origin is same for both setup.

========

b) horizontal electric field

Eh = k q /r^2 = 9*10^9* 5*10^-6 / ( 0.061^2) = 1.21*10^7

vertical electric field

Ev = k q / r^2 = 9*10^9* 5*10^-6/ 0.061^2 =1.21*10^7

net magnitude of electric field

E^2 = Ev^2 + Eh^2

E = 1.71*10^7 N/C

direction,

phi = arctan ( Ev / Eh)

phi = 45 deg

========

do comment in case any doubt, will reply for sure. Goodluck