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Chapter 19: Problem 2

Lightning strikes. During lightning strikes from a cloud to the ground, currents as high as \(25,000\) A can occur and last for about 40\(\mu\) s. How much charge is transferred from the cloud to the earth during such a strike?

Short Answer

Expert verified
1 coulomb of charge is transferred.

Step by step solution

01

Identify Given Values

We are given that the current, denoted by \( I \), is \( 25,000 \) A and the time duration of the current, denoted by \( t \), is \( 40 \mu s \), which is equivalent to \( 40 \times 10^{-6} \) seconds.
02

Understand the Relationship Between Charge, Current, and Time

The relationship between charge \( Q \), current \( I \), and time \( t \) is given by the formula \( Q = I \times t \). This equation expresses that the charge transferred is equal to the product of current and time duration.
03

Calculate the Charge

Substitute the given values into the equation: \[ Q = 25,000 \times (40 \times 10^{-6}) \]Performing the multiplication gives:\[ Q = 25,000 \times 40 \times 10^{-6} = 1 \] This result means that 1 coulomb of charge is transferred.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Current in Physics
In physics, current is a fundamental concept related to the flow of electric charge. It's often measured in amperes (A), where one ampere corresponds to the flow of one coulomb of charge per second. The current tells us how much charge moves through a point in a circuit over time. It's like the flow of water, where more current means a larger flow of charge.

When we discuss electric current, it's important to consider both its direction and magnitude.
  • Direction: Current flows from a point of high potential energy (positive) to a point of low potential energy (negative) in a circuit.
  • Magnitude: Indicates the amount of charge flow per unit time.
Understanding current helps us predict how circuits behave and is essential when calculating how much charge moves in a given time, such as during a lightning strike. The current during a lightning strike can be enormous, often reaching as high as 25,000 A, as in our problem.
Charge Transfer
Charge transfer is the movement of electric charge from one place to another. In the context of circuits, this often involves the flow of electrons through conductive materials. The amount of charge transferred can be calculated by using the relationship between current, time, and charge.
  • Formula: The basic formula used to calculate the amount of charge, expressed in coulombs (C), is \( Q = I \times t \), where \( Q \) is the charge, \( I \) is the current, and \( t \) is the time.
  • Application: By knowing the current and the duration for which it flows, we can determine how much charge is transferred.
Let's consider lightning strikes, where we have a high current for a brief moment. By multiplying that current by the time it lasts, we can find the total charge transferred during the strike. In the example, we found that a lightning strike transmits 1 coulomb of charge between the cloud and the ground.
Lightning Strike Electricity
Lightning strikes are fascinating natural occurrences involving immense electrical forces. They serve as a dramatic example of electrical phenomena, illustrating the concept of charge transfer on a grand scale.

During a lightning strike, an enormous amount of charge is rapidly transferred from the cloud to the ground.
  • High Current: These strikes involve exceptionally high currents, often exceeding tens of thousands of amperes, as we calculated to be 25,000 A in this scenario.
  • Brief Duration: The strike lasts only for fractions of a second, usually in the range of milliseconds to microseconds.
The rapid discharge of electrical energy in a lightning strike can transfer around 1 coulomb of charge in a short time, as we observed in our solution. This immense and rapid exchange of electrical charge is what leads to the intense light and sound鈥攊ncluding thunder鈥攁ssociated with lightning.

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Most popular questions from this chapter

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