For the lightning strike simulator described in the passage, the distance between the person electrode and the cloud electrode is 3 m. Assume that the electrodes behave like point charges. What is the maximum charge on the cloud electrode when the electrical breakdown limit of air is reached? (Note: Coulomb's constant is k = 9 × 109 N∙m2/C2.)A.9 mCB.3 mCC.1 mCD.0.3 mC
Question
For the lightning strike simulator described in the passage, the distance between the person electrode and the cloud electrode is 3 m. Assume that the electrodes behave like point charges. What is the maximum charge on the cloud electrode when the electrical breakdown limit of air is reached? (Note: Coulomb's constant is k = 9 × 109 N∙m2/C2.)A.9 mCB.3 mCC.1 mCD.0.3 mC
Solution
The electrical breakdown of air occurs when the electric field between the electrodes reaches a critical value, which is approximately 3 x 10^6 N/C. The electric field E between two point charges is given by Coulomb's law:
E = kQ/r^2
where:
- E is the electric field,
- k is Coulomb's constant (9 x 10^9 N*m^2/C^2),
- Q is the charge on one of the points (in this case, the cloud electrode), and
- r is the distance between the points (3 m in this case).
We can rearrange this equation to solve for Q:
Q = E*r^2/k
Substituting the given values:
Q = (3 x 10^6 N/C) * (3 m)^2 / (9 x 10^9 N*m^2/C^2) Q = 9 x 10^-4 C
So, the maximum charge on the cloud electrode when the electrical breakdown limit of air is reached is 0.9 mC, which corresponds to option A.
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