During a thunderstorm, the separation between the clouds and the earth acts as a giant capacitor with a capacitance of 2,500 µF (µ is the SI prefix for 10-6). If a tower is struck by a lightning bolt that releases 50 C of charge, how much energy is released?
To calculate the amount of energy released during a lightning strike, we can use the formula:
Energy (E) = (1/2) * C * V^2
Where:
C is the capacitance of the capacitor (2,500 µF or 2,500 * 10^-6 F)
V is the voltage across the capacitor (which will be the potential difference between the clouds and the earth)
Unfortunately, the problem does not provide us with the voltage (V) value directly. However, we can make use of another formula to find it, by considering the charge (Q) stored on the capacitor:
Charge (Q) = C * V
Rearranging the equation, we get:
V = Q / C
Now we can substitute this expression for V back into the initial energy equation:
E = (1/2) * C * (Q / C)^2
Simplifying further:
E = (1/2) * C * Q^2 / C^2
E = (1/2) * Q^2 / C
Now we can plug in the given values:
Q = 50 C
C = 2,500 µF = 2,500 * 10^-6 F
Substituting these values into the equation:
E = (1/2) * (50)^2 / (2,500 * 10^-6)
Calculating further:
E = (1/2) * (2,500) / (2,500 * 10^-6)
E = 1 / (2 * 10^-6)
E = 1 / (2 * 10^-6)
E = 1 / (2 * (1/10^6))
E = 1 / (2 * 10^6)
E = 5 * 10^-7 J
Therefore, the energy released during the lightning strike is approximately 5 * 10^-7 Joules.