Problem 4 - Fundamentals of Physics

Question

In the return stroke of a typical lightning bolt, a current of \(2.5 \times 10^{4}\) A exists for \(20 \mu\) s. How much charge is transferred in this event?

Step-by-Step Solution

Answer

The charge transferred is 0.5 Coulombs.

Step 1: Understand the Relationship

To find out the amount of charge transferred, we need to use the relationship between current, charge, and time: \[ Q = I imes t \]where \( Q \) is the charge, \( I \) is the current, and \( t \) is the time.

Step 2: Identify the Variables

Here, we have:- Current \( I = 2.5 \times 10^{4} \) A,- Time \( t = 20 \mu s = 20 \times 10^{-6} \) s.

Step 3: Apply the Formula

Substitute the known values into the equation:\[ Q = 2.5 \times 10^{4} \times 20 \times 10^{-6} \]

Step 4: Calculate the Charge

Simplify and calculate the expression:\[ Q = 2.5 \times 20 \times 10^4 \times 10^{-6} \]\[ Q = 50 \times 10^{-2} \]\[ Q = 0.5 \, C \]

Step 5: Review the Solution

The charge transferred during this lightning event is calculated as \(0.5 \) Coulombs.

Key Concepts

Understanding Electrical Current

In electrical terms, current is the flow of electric charge through a conductor, such as a wire. Imagine it as water flowing through a pipe, where the amount of water (electric charge) flowing per second is the current.

The unit of current is the ampere, often shortened to "A." When we say that a lightning strike has a current of \(2.5 \times 10^{4}\) A, it means 25,000 units of charge are passing through a point in the lightning bolt per second.

To calculate the charge passing through, you multiply the current by the time the current is flowing. This relationship is given by the formula:

• The formula: \(Q = I \times t\) where \(Q\) is the charge in coulombs.
• \(I\) is the current in amperes, and
• \(t\) is the time in seconds.

This basic principle helps us understand how much charge moves through a system over a given period.

The Power of Lightning

Lightning is a powerful natural phenomenon involving the rapid movement of electric charges. It is a dramatic illustration of electric current in action.

A typical lightning bolt can carry a massive current, such as \(2.5 \times 10^{4}\) amperes as seen in the problem above. This huge flow of electric charge results from the clouds building up opposite charges, which eventually meet, causing an electric discharge.

The duration of this current flow is extremely short, often just a few microseconds (a microsecond is \(10^{-6}\) seconds). During that brief period, a tremendous amount of electrical energy is transferred, sometimes enough to start fires, split trees, or cause damage to structures. Understanding the behavior of lightning as a current gives us insight into both its power and its dangers.

The Role of Time Duration in Charge Transfer

Time duration indicates how long a current flows through a conductor. In our lighting example, the time duration is expressed in microseconds (\(\mu s\)), where \(1\,\mu s = 10^{-6}\,s\).

In the formula \(Q = I \times t\), time duration is a crucial factor because it determines how much charge is transferred over that specific period. Even massive currents, when only existing for brief moments, transfer limited charge due to short time durations.

For instance, with a current of \(2.5 \times 10^4\) A flowing for \(20\,\mu s\), the total charge transferred is simplified to \(0.5\) Coulombs as calculated earlier.

This shows that the relationship between current and time determines the magnitude of charge movement, underlining the significance of time duration in electrical events.