You've decided to protect your house by placing a 5.0-m-tall iron lightning rod next to the house. The top is sharpened to a point and the bottom is in good contact with the ground. From your research, you've learned that lightning bolts can carry up to 50 kA of current and last up to 50 μs. How much charge is delivered by a lightning bolt with these parameters?

검증된 단계별 안내

Identify the given values: The current carried by the lightning bolt is \( I = 50 \text{kA} = 50,000 \text{A} \), and the duration of the lightning bolt is \( t = 50 \mu\text{s} = 50 \times 10^{-6} \text{s} \).

Recall the relationship between charge, current, and time: \( Q = I \cdot t \), where \( Q \) is the charge, \( I \) is the current, and \( t \) is the time.

Substitute the given values into the formula: \( Q = (50,000 \text{A}) \cdot (50 \times 10^{-6} \text{s}) \).

Simplify the expression by multiplying the current and time to calculate the total charge delivered by the lightning bolt.

Express the result in coulombs (C), as charge is measured in this unit, and ensure the final value is in proper scientific notation if necessary.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Current

Current is the flow of electric charge in a circuit, measured in amperes (A). In the context of lightning, the current can be extremely high, as indicated by the 50 kA mentioned in the question. This high current results from the rapid movement of electrons during a lightning strike, which can deliver a significant amount of energy in a very short time.

Charge

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. Charge is measured in coulombs (C). The total charge delivered by a lightning bolt can be calculated using the formula Q = I × t, where Q is the charge, I is the current, and t is the time duration of the current flow.

Time Duration

Time duration refers to the length of time that an event occurs. In the case of a lightning strike, the duration is typically very short, often in the microsecond range, as indicated by the 50 μs in the question. This brief time frame is crucial for calculating the total charge delivered, as it directly influences the amount of charge that flows during the lightning event.