A $1.00 \mathrm{nC}$ charge is placed on the $\mathrm{x}$-axis at $\mathrm{x}=-1.00 \mathrm{~m}$. A second $1.00 \mathrm{nC}$ charge is placed on the $\mathrm{x}$-axis at $\mathrm{x}=1.00 \mathrm{~m}$. A third charge of $1.00 \mathrm{nC}$ is placed on the $\mathrm{y}$-axis at $\mathrm{y}=-1.00 \mathrm{~m}$. A fourth charge is place on the $y$-axis at $y=1.00 \mathrm{~m}$. What is the fourth charge if the electric field at the origin is zero?

Question

Quizplus · Accepted Answer

For the electric field at the origin to be zero, the net force due to the electric fields from all charges must cancel out. The charges on the x-axis create electric fields that cancel each other out because they are equal in magnitude and opposite in direction. Similarly, for the charges on the y-axis to cancel out, the fourth charge must also be $1.00 \mathrm{nC}$, making it equal in magnitude and opposite in direction to the charge at $y = -1.00 \mathrm{m}$.

A 1.00nC1.00 \mathrm{nC}1.00nC Charge Is Placed on The x\mathrm{x}x -Axis At x=−1.00 m\mathrm{x}=-1.00 \mathrm{~m}x=−1.00 m

A $1.00 \mathrm{nC}$ Charge Is Placed on The $\mathrm{x}$ -Axis At $\mathrm{x}=-1.00 \mathrm{~m}$