A positive charge Q1,-45.5 nC is located at the origin. A negative charge Q2 =-5.5 nC is located on the positive x-axis, p = 14 cm from the origin. Choose the correct relation to indicate the continuous region on the x-axis that includes a point where the electric field is zero.

Answer:  r = 0.1045 cmExplanation:The electric field of a point charge is given by the expression           E = k q / r² Let's look for the field created by each load Q₁ charge            E₁ = k Q₁ / (r-0)²            E₁ = - 8.99 10⁹ 45.5 10⁻⁹ / r²            E₁ = - 409.05 / r² Q₂ charge            E₂ = k Q₂ / (r-0.14)₂            E₂ = - 8.99 10⁹ 5.5 10⁻⁹ / (r-0.14)²            E₂ = -49.45 / (r-0.14)² The electric field is a vector quantity, so we must use the sum of vectors to get the total field            E_total = E₁ + E₂ The burden of proof is always considered positive as the two charges are negative the strength is attractive, consider three regions of interest. - Left of the two charges in this case the two forces are directed to the right and therefore the field is not canceled - to the right of the two charges, the forces go to the left and the field is not canceled for any distance - Between the two charges, in this case each force goes in the opposite direction and there is a point for the field to cancel              0 = E₁ - E₂              E₁ = E₂             -409.05 / r² = - 49.45 /(r-0.14)²               (r-0.14)² = 49.45 / 409.05 r²              r² - 2 0.14r + 0.14² = 0.12 r²              r² (1-0.12) - 0.28 r + 0.0196 = 0              0.88 r² - 0.28 r + 0.0196 = 0              r² - 0.318 r + 0.0223 = 0 We solve the second degree equation             r = [0.318 ±√(0.318² - 4 0.0223)] / 2             r = [0.318 ± 0.109] 2             r₁ = 0.209 / 2 = 0.1045 m             r₂ = 0.2135 m We see that the result in the area of ​​interest between charges is              r = 0.1045 cm               - There are zones on the sides of the charge, but the force in these zones has a component that takes the test load to the part between the loads, therefore the field is never canceled