5. gather data: turn on show angle. for each combination of charges in the table below, record the product…

5. gather data: turn on show angle. for each combination of charges in the table below, record the product of the two charges and the resulting angle. (note: if you like, you can type the charge values directly into the text boxes to the right of each slider and hit “enter.”)\n| q₁ | q₂ | q₁×q₂ | angle |\n|----|----|----|----|\n| 6.0×10⁻⁶ c | 4.0×10⁻⁶ c | | |\n| 8.0×10⁻⁶ c | 3.0×10⁻⁶ c | | |\n| 16.0×10⁻⁶ c | 1.0×10⁻⁶ c | | |\n| -4.0×10⁻⁶ c | -4.0×10⁻⁶ c | | |\n6. analyze: how does the electrostatic force relate to the product of the charges? explain.

5. gather data: turn on show angle. for each combination of charges in the table below, record the product of the two charges and the resulting angle. (note: if you like, you can type the charge values directly into the text boxes to the right of each slider and hit “enter.”)\n| q₁ | q₂ | q₁×q₂ | angle |\n|----|----|----|----|\n| 6.0×10⁻⁶ c | 4.0×10⁻⁶ c | | |\n| 8.0×10⁻⁶ c | 3.0×10⁻⁶ c | | |\n| 16.0×10⁻⁶ c | 1.0×10⁻⁶ c | | |\n| -4.0×10⁻⁶ c | -4.0×10⁻⁶ c | | |\n6. analyze: how does the electrostatic force relate to the product of the charges? explain.

Answer

Explanation:

Step1: Calculate product of charges for each row

For the first row: $q_1 = 6.0\times10^{- 6}\text{C}$, $q_2=4.0\times10^{-6}\text{C}$, then $q_1\times q_2=(6.0\times10^{-6})\times(4.0\times10^{-6}) = 24\times10^{-12}=2.4\times 10^{-11}\text{C}^2$ For the second row: $q_1 = 8.0\times10^{-6}\text{C}$, $q_2 = 3.0\times10^{-6}\text{C}$, then $q_1\times q_2=(8.0\times10^{-6})\times(3.0\times10^{-6})=24\times10^{-12} = 2.4\times10^{-11}\text{C}^2$ For the third row: $q_1=16.0\times10^{-6}\text{C}$, $q_2 = 1.0\times10^{-6}\text{C}$, then $q_1\times q_2=(16.0\times10^{-6})\times(1.0\times10^{-6})=16\times10^{-12}=1.6\times10^{-11}\text{C}^2$ For the fourth row: $q_1=-4.0\times10^{-6}\text{C}$, $q_2=-4.0\times10^{-6}\text{C}$, then $q_1\times q_2=(-4.0\times10^{-6})\times(-4.0\times10^{-6}) = 16\times10^{-12}=1.6\times10^{-11}\text{C}^2$ The angle values are not provided in the problem - statement to calculate, but according to Coulomb's law $F = k\frac{q_1q_2}{r^2}$, the electrostatic force $F$ is directly proportional to the product of the two charges $q_1$ and $q_2$ when the distance $r$ between the charges is constant. That is, as the product $q_1q_2$ increases, the electrostatic force between the two charges increases, and vice - versa.

Answer:

$q_1$ $q_2$ $q_1\times q_2$ Angle (not calculated)
$6.0\times10^{-6}\text{C}$ $4.0\times10^{-6}\text{C}$ $2.4\times10^{-11}\text{C}^2$ N/A
$8.0\times10^{-6}\text{C}$ $3.0\times10^{-6}\text{C}$ $2.4\times10^{-11}\text{C}^2$ N/A
$16.0\times10^{-6}\text{C}$ $1.0\times10^{-6}\text{C}$ $1.6\times10^{-11}\text{C}^2$ N/A
$-4.0\times10^{-6}\text{C}$ $-4.0\times10^{-6}\text{C}$ $1.6\times10^{-11}\text{C}^2$ N/A
The electrostatic force is directly proportional to the product of the charges when the distance between them is constant.