Question

a charge of -6.0 uC is at x = 0 and a 2.0- uC charge is at x = 6.0 cm. what is the electric field at x = 4.0 cm? specify the direction with the sign

will rate well

Answer 1

charge q₁ = -6μC = -6 x 10^-6 C

charge q₂ = 2μC = 2 x 10^-6 C

distance of charge q₁ from the point X is r₁ = 4 cm = 0.04 m

distance of charge q₂ from the point X is r₂ = 6-4 cm =2 cm= 0.02 m

electric field at a point due to a point charge, E = 1/4πε₀ q/r²

electric field at the point X due to charge q₁ is

E₁ = 1/4πε₀ q/r₁² = 9 x 10⁹ x 6 x 10^-6 /0.04 x 0.04 = 33.75 x 10⁶ N/C acts along - ve X – axis

electric field at the point X due to charge q₂ is

E₂ = 1/4πε₀ q/r₂² = 9 x 10⁹ x 2 x 10^-6 /0.02 x 0.02 = 45.0 x 10⁶ N/C acts along - ve X – axis

Resultant electric field at the point X is E = E₁ + E₂ = 33.75 x 10⁶ + 45.0 x 10⁶ = 78.75 x 10⁶ N/C

Resultant electric field at the point X is E = 78.75 x 10⁶ N/C and it acts along – X -axis