Question

1. the diagram below shows the arrangement of three small spheres, a, b, and c, having charges of 3q, q, and q, respectively. spheres a and c are located distance r from sphere b. a 3q • b q • c q • |<--- r --->|<--- r --->| compared to the magnitude of the electrostatic force exerted by sphere b on sphere c, is the magnitude of the electrostatic force exerted by sphere a on sphere c (a) the same, (b) 3/4 as great, (c) twice as great, or (d) 3/2 as great?

Explanation:

Step1: Recall Coulomb's law

The electrostatic force between two charges $q_1$ and $q_2$ separated by a distance $r$ is given by $F = k\frac{q_1q_2}{r^{2}}$, where $k$ is the Coulomb's constant.

Step2: Calculate force of B on C

The force exerted by Sphere B on Sphere C, $F_{BC}=k\frac{q\times q}{r^{2}}=k\frac{q^{2}}{r^{2}}$.

Step3: Calculate force of A on C

The distance between Sphere A and Sphere C is $2r$. The force exerted by Sphere A on Sphere C, $F_{AC}=k\frac{3q\times q}{(2r)^{2}}=k\frac{3q^{2}}{4r^{2}}$.

Step4: Find the ratio

$\frac{F_{AC}}{F_{BC}}=\frac{k\frac{3q^{2}}{4r^{2}}}{k\frac{q^{2}}{r^{2}}}=\frac{3}{4}$.

Answer:

(b) 3/4 as great