Problem 2 - University Physics with Modern Physics

Question

Lightning occurs when there is a flow of electric charge (principally electrons) between the ground and a thundercloud. The maximum rate of charge flow in a lightning bolt is about \(20,000 \mathrm{C} / \mathrm{s} ;\) this lasts for 100\(\mu\) or less. How much charge flows between the ground and the cloud in this time? How many electrons flow during this time?

Step-by-Step Solution

Answer

2 C charge flows, with about 1.25 × 10^19 electrons.

Step 1: Understand the problem

We need to determine the amount of charge that flows during a lightning bolt and the number of electrons that correspond to this charge. The rate of charge flow given is \(20,000\, \mathrm{C/s}\), which occurs for \(100\, \mu s\).

Step 2: Calculate Charge Flow

The formula for charge flow is \(Q = I \times t\), where \(I\) is the current (\(20,000\, \mathrm{C/s}\)) and \(t\) is the time (\(100\, \mu s\) which is \(0.0001\, \mathrm{s}\)). Substitute the values:\[ Q = 20,000 \times 0.0001 = 2\, \text{Coulombs} \]

Step 3: Calculate Number of Electrons

To find the number of electrons, use the formula \(n = \frac{Q}{e}\), where \(e = 1.6 \times 10^{-19}\, \mathrm{C}\) is the elementary charge of an electron. Substitute the values:\[ n = \frac{2}{1.6 \times 10^{-19}} = 1.25 \times 10^{19}\, \text{electrons} \]

Step 4: Conclusion

The total charge that flows between the cloud and ground is \(2\, \mathrm{C}\), and approximately \(1.25 \times 10^{19}\) electrons flow in this process.

Key Concepts

lightning

Lightning is a powerful natural phenomenon characterized by a sudden discharge of electricity. It typically occurs during thunderstorms when there is an imbalance of electric charges between storm clouds and the ground. These electric discharges lead to the rapid heating and expansion of air, producing the sound we know as thunder. Lightning can travel at speeds of up to one-third the speed of light, making it one of the fastest natural events.

• Lightning is crucial for balancing electrical charges in the atmosphere.
• It occurs primarily due to the process by which electrical charges build up in storm clouds.
• The path of lightning is shaped by the differing air conditions and the charge distribution in clouds and on the ground.

Understanding this process can help in developing better safety measures against lightning strikes.

electric charge

An electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. Charges are of two types: positive and negative. In the context of lightning, electric charges build up within clouds due to the movement of water droplets and ice crystals.

• Positive charges tend to accumulate at the top of the cloud, while negative charges gather at the bottom.
• This separation of charges creates the perfect condition for lightning to occur.
• When the electric field becomes strong enough, it overcomes the air's resistance, allowing negative charges to flow to the ground as lightning.

The balance between positive and negative charges is crucial in preventing electric discharges like lightning.

current flow

Current flow refers to the movement of electric charge, usually measured in amperes. In our context, lightning represents an extremely high current flow, translating into a brief yet immense transfer of energy.

• The current in a lightning strike can be upwards of 20,000 amperes, making it highly destructive.
• This massive flow only lasts a fraction of a second, usually just milliseconds.
• The intensity of the current flow is responsible for the incredible power and brightness of lightning.

Understanding current flow helps in grasping why lightning can be so dangerous and how we might work to mitigate its impact.

electrons

Electrons are subatomic particles with a negative electric charge. They play a crucial role in many physical phenomena, including electricity and magnetism. In the process of a lightning strike, it's mainly electrons that move between the cloud and the ground.

• An electron's charge is approximately \(1.6 \times 10^{-19} \) Coulombs.
• The number of electrons involved in a typical lightning bolt is immense, reaching up to \(1.25 \times 10^{19}\) electrons.
• Because electrons are so small and numerous, they can create a significant current even over a brief period.

Grasping the role of electrons allows for a deeper understanding of how electrical currents operate on a microscopic scale.