Two charges Q₁ and Q₂ are a distance d apart.If the electric field is zero at a distance of 3d/4 from Q₁ (towards Q₂),then what is the relation between Q₁ and Q₂? A)Q₁ = Q₂/9 B)Q₁ = 9Q₂ C)Q₁ = Q₂/3 D)Q₁ = 3Q₂ E)Q₁ = 4Q₂/3

Question

Quizplus · Accepted Answer

The electric field is zero at a point between two charges when the magnitudes of the electric fields due to each charge are equal at that point. The electric field due to a charge is given by $E = k\frac{Q}{r^2}$, where $E$ is the electric field, $k$ is Coulomb's constant, $Q$ is the charge, and $r$ is the distance from the charge. If the electric field is zero at a distance of $3d/4$ from $Q_{₁}$ towards $Q_{₂}$, then the distance from $Q_{₂}$ is $d - 3d/4 = d/4$. Setting the magnitudes of the electric fields equal to each other and solving for the ratio of the charges gives $Q_{₁} = 9Q_{₂}$, because the distance from $Q_{₁}$ is squared in the denominator, making the ratio of the distances squared (i.e., $(3d/4)^2 / (d/4)^2 = 9$).

Two Charges Q1 and Q2 Are a Distance D Apart

Two Charges Q₁ and Q₂ Are a Distance D Apart