Question

I’m not sure where to go from here21. Using your measurements and your force equations, experimentally determine the charge on Charge Two. Show your work below.

Answer 1

35.1 nC

Step-by-step explanation

First, we have to determine the equations:

In the force diagram above, the coordinate system drawn in green is used - note that this is one of the possible options. Using that coordinate system, we have that the weight of the charge is not parallel to either axis, so it must be decomposed to write the y and x equations,

`\begin{cases}x:F_q=mg\sin\theta{} \\ y:F_T=mg\cos\theta{}\end{cases}`

It was measured that the mass of the charge was 0.084 g = 0.000084 kg, and the measured angle is 24.5°, so Coulomb's force is,

`Fq=0.000084g\cdot9.81m/s^2\cdot\sin24.5\degree\approx3.42\cdot10^(-4)N`

This force is also equal to,

`F_q=k(q_1q_2)/(d^2)`

Where k is Coulomb's constant, with a value of 9.0 x 10⁹ Nm²/C², q₁ and q₂ are the charges and d is the distance between the charges.

Let's solve this equation for q₂,

`q_2=(F_qd^2)/(kq_1)`

If the measured distance between the charges was 19 cm, which is equivalent to 0.19 m, and charge one is 39.1 nC,

`q_2=(3.42\cdot10^(-4)N\cdot0.19^2m^2)/(9\cdot10^9Nm^2/C^2\cdot39.1\cdot10^(-9)C)\approx35.1\cdot10^(-9)C=35.1nC`

Hence, the charge in Charge Two is 35.1 nC, given that the charge in Charge One is 39.1 nC as shown in the simulation.