A charge Q₁ = Q is positioned on the x axis at x = a.Where should a charge Q₂ = 9Q be placed to produce a net electric force of zero on a charge placed at the origin? A)at x = 2a B)at x = -2a C)at x = 3a D)at x = -3a E)at x = 4a

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Quizplus · Accepted Answer

For the net electric force on a charge placed at the origin to be zero, the forces exerted by the two charges on this charge must be equal in magnitude but opposite in direction. The force between two charges is given by Coulomb's law, $F = k \frac{|q_1 q_2|}{r^2}$, where $k$ is Coulomb's constant, $q_1$ and $q_2$ are the magnitudes of the charges, and $r$ is the distance between the charges.Given that one charge $Q$ is at $x = a$ and the other charge $9Q$ needs to be placed such that the net force on a charge at the origin is zero, we can deduce that the charge $9Q$ must be placed further away from the origin than $Q$ because it has a larger magnitude and would exert a stronger force if placed at the same distance as $Q$.The distance from the origin at which the force from $9Q$ equals the force from $Q$ in magnitude but is in the opposite direction can be found by setting the forces equal:$$k \frac{Q \cdot Q}{a^2} = k \frac{9Q \cdot Q}{x^2}$$Simplifying, we get:$$1 = \frac{9}{(\frac{x}{a})^2}$$Solving for $\frac{x}{a}$, we find:$$\frac{x}{a} = 3$$Therefore, $x = 3a$. Since we need the force from $9Q$ to oppose the force from $Q$, and knowing that $Q$ is placed at $x = a$ (to the right of the origin), $9Q$ must be placed to the left of the origin to exert a force towards the origin. Thus, the correct position is $x = -3a$.

A Charge Q1 = Q Is Positioned on the X

A Charge Q₁ = Q Is Positioned on the X