Question

a. For point charge 5.4 µC and point charge -3.6 µC located at the same positions as in the previous question (5 m and 4 m, respectively), determine the magnitude of the net electric field E at the origin (in N/C).

Your answer should be a number with two decimal places, do not include the unit.

b. For point charge -1.4 µC and point charge 5.8 µC located at the same positions as in the previous question (5 m and 4 m, respectively), determine the direction of the net electric field E at the origin.

1µC = 10-6C

Your answer should be an integer, do not include the unit.

Answer 1

a)

Q₁ = 5.4 x 10^-6 C

Q₂ = - 3.6 x 10^-6 C

r₁ = distance of charge Q₁ from the origin = 5 m

r₂ = distance of charge Q₂ from the origin = 4 m

Electric field at the origin by charge Q₁ is given as

E₁ = k Q₁/r₁² = (9 x 10⁹) (5.4 x 10^-6)/5² = 1944 N/C

Electric field at the origin by charge Q₂ is given as

E₂ = k Q₂/r₂² = (9 x 10⁹) (3.6 x 10^-6)/4² = 2025 N/C

Taking the electric fields in left as negative and in right direction as positive, net electric field at the origin is given as

E = E₂ - E₁ = 2025 - 1944 = 82 N/C

b)

Q₁ = - 1.4 x 10^-6 C

Q₂ = 5.8 x 10^-6 C

r₁ = distance of charge Q₁ from the origin = 5 m

r₂ = distance of charge Q₂ from the origin = 4 m

Electric field at the origin by charge Q₁ is given as

E₁ = k Q₁/r₁² = (9 x 10⁹) (1.4 x 10^-6)/5² = 504 N/C

Electric field at the origin by charge Q₂ is given as

E₂ = k Q₂/r₂² = (9 x 10⁹) (5.8 x 10^-6)/4² = 3262.5 N/C

Taking the electric fields in left as negative and in right direction as positive, net electric field at the origin is given as

E = - E₂ + E₁ = - 3262.5 + 504 = - 2758.5 N/C

the negative sign indicates that the net electric field is in negative x-direction