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# Charges and Their Interactions

The motion of charged matter underlies many things we enjoy like phones and plasma globes. It also puts a permanent end to the enjoyment of some 6,000 people per year, as fatal lightning strikes.

Let \( \pi \approx 3 \) and the permitivity of free space \( \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2} \)

Two charges Q=+1 mC are placed along the x-axis at x=-2 meters and x=2 meters. The charges are fixed in space. A third charge, which is free to move and has charge q=-0.1 mC and mass m=1g, is placed along the y-axis at y=0.01 meters and released. How long does it take **in seconds** for the charge to come back to y=0.01?

**Details and assumptions**

- \(k=(4 \pi \epsilon_0)^{-1}= 9 \times 10^9~Nm^2/C^2\)

Let \( \pi \approx 3 \) and the permitivity of free space \( \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2} \)

A test charge \( Q = 5 \times 10^{-6} \text{ C } \) is placed by a single point charge \( q = 7 \times 10^{-6} \text{ C } \) which is at rest at a distance of \( r = 4 \text{ m } \) away. If the force can be expressed as \( F = \frac{a}{b} \text{ N}, \) where \(a\) and \(b\) are coprime positive integers, what is the value of \(a+b?\)

Let \( \pi \approx 3 \) and the permitivity of free space \( \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2} \)

If the magnitude of the electric field at a distance of \( r = 3 \text{ m}\) from the point charge \( Q = 9 \times 10^{-12} \text{ C } \) can be expressed as \( E = \frac{a}{b} \text{ N/C}, \) where \(a\) and \(b\) are coprime positive integers, what is the value of \(a+b?\)

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