Two charges are located on the x-axis. A 22 µC charge is located at the origin and a 47 µC charge is located at x = 4.0 m. What is the magnitude of the electric field at x = 7.5 m? A) 4.0 × 10⁵ N/C B) 3.8 × 10⁴ N/C C) 5.7 × 10⁵ N/C D) 6.3 × 10⁴ N/C E) 2.5 × 10⁶ N/C

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Quizplus · Accepted Answer

The electric field (E) due to a point charge (q) at a distance (r) is given by Coulomb's law, $E = \frac{kq}{r^2}$, where $k = 9.0 \times 10^9 \, \text{N m}^2/\text{C}^2$. For the 22 µC charge at the origin, the distance to the point at x = 7.5 m is 7.5 m. For the 47 µC charge at x = 4.0 m, the distance to the point at x = 7.5 m is 3.5 m. Calculate the electric field due to each charge separately and then add them vectorially, considering their directions (towards or away from each charge). The correct magnitude, considering the given options and typical calculations, matches the value in choice B, which suggests a careful calculation and vector addition of the fields from each charge.

Two Charges Are Located on the X-Axis