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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 \( \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}. \)

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

A point particle with mass \( m = 1 \text{ kg}\) and charge \( q = -7\times 10^{-6} \text{ C } \) is rotating around another point particle with charge \( Q = 7\times 10^{-6} \text{ C } \),which is fixed at the center, with radius \( r = 2 \text{ m}\). If the speed of the circular motion can be expressed as \( v = \sqrt{\frac{a}{b}} \text{ m/s}, \) 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 \( \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}. \)

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

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