Three charges are located at 100-m intervals along a horizontal line: a charge of -3.0 C on the left, 2.0 C in the middle, and 1.0 C on the right. What is the electric field on the horizontal line halfway between the -3.0 C and 2.0 C charges?

Question

Three charges are located at 100-m intervals along a horizontal line: a charge of -3.0 C on the left, 2.0 C in the middle, and 1.0 C on the right. What is the electric field  on the horizontal line halfway between the -3.0 C and 2.0 C charges?

Quizplus · Accepted Answer

Using the equation for electric field at a point due to a point charge, $E = \frac{kQ}{r^2}$ where $k$ is Coulomb's constant, $Q$ is the charge, and $r$ is the distance from the point charge. First, finding the electric field at the midpoint between the -3.0 C and 2.0 C charges: $E_{midpoint} = \frac{k(-3.0 ext{ C})}{(50 ext{ m})^2} + \frac{k(2.0 ext{ C})}{(50 ext{ m})^2}$ $E_{midpoint} = 1.8 imes10^9 ext{ N/C}$ to the left Then, finding the electric field at the midpoint between the 2.0 C and 1.0 C charges: $E_{midpoint} = \frac{k(2.0 ext{ C})}{(50 ext{ m})^2} + \frac{k(1.0 ext{ C})}{(50 ext{ m})^2}$ $E_{midpoint} = 6.4 imes10^8 ext{ N/C}$ to the right Therefore, the net electric field at the midpoint of the -3.0 C and 2.0 C charges due to all three charges is: $E_{net} = E_{midpoint\;between\;-3.0C\;and\;2.0C} + E_{midpoint\;between\;2.0C\;and\;1.0C}$ $E_{net} = (1.8 imes10^9 ext{ N/C to the left}) + (6.4 imes10^8 ext{ N/C to the right})$ $E_{net} = 1.2 imes10^9 ext{ N/C to the left}$ Therefore, the best choice is (C), 1.8 F1F1F1S1F1F1F10 10⁷ N/C to the left.

Three Charges Are Located at 100-M Intervals Along a Horizontal