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Chapter 21: Problem 2

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\(\mu \mathrm{s}\) or less. How much charge flows between the ground and the cloud in this time? How many electrons flow during this time?

Short Answer

Expert verified
2 Coulombs of charge flow; about \(1.25 \times 10^{19}\) electrons.

Step by step solution

01

Convert Time from Microseconds to Seconds

The time given is in microseconds (\(100\, \mu\mathrm{s}\)). Convert this to seconds by using the conversion \(1\, \mu\mathrm{s} = 1 \times 10^{-6}\, \mathrm{s}\).\[100\, \mu\mathrm{s} = 100 \times 10^{-6}\, \mathrm{s} = 0.0001\, \mathrm{s}\]
02

Calculate Charge Flow

To find the charge that flows, use the formula:\[Q = I \times t\]where \(I = 20,000\, \mathrm{C/s}\) (electric current), and \(t = 0.0001\, \mathrm{s}\) (time).\[Q = 20,000 \times 0.0001 = 2\, \mathrm{C}\]So, 2 Coulombs of charge flow between the ground and the cloud.
03

Calculate Number of Electrons

Use the charge of a single electron, \(e = 1.6 \times 10^{-19}\, \mathrm{C}\),to find out how many electrons correspond to a charge of 2 Coulombs.The number of electrons \(N\) can be calculated as:\[N = \frac{Q}{e} = \frac{2}{1.6 \times 10^{-19}} \approx 1.25 \times 10^{19}\]Therefore, approximately \(1.25 \times 10^{19}\) electrons flow during this time.

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Key Concepts

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

Lightning
When the sky lights up during a thunderstorm, it's not just a bright flash; it's an incredible display of nature's power and the movement of electric charge.
Lightning occurs as a discharge of electricity between a thundercloud and the ground, or even between clouds.
This phenomenon happens when there is an enormous difference in electrical charge, known as potential difference, which creates an electric field strong enough to overcome the air's insulating properties.
A few crucial points about lightning include:
  • Lightning strikes are rapid, often lasting less than 100 microseconds.
  • The electric current during a lightning strike can peak at around 20,000 Coulombs per second.
  • This immense electric charge is mainly due to electrons traveling between the cloud and the ground.
Understanding lightning involves studying the flow of electric charge and how a balance is eventually achieved through the powerful strike we witness when a thunderstorm rolls through.
Electric Current
Electric current is essentially the flow of electric charge.
In the context of lightning, it refers to the movement of electrons from one region to another, creating a path for electricity to flow.
The strength or rate of this flow is measured in Amperes (A), though a lightning current is phenomenally high compared to everyday electrical currents.
For lightning:
  • Even a brief lightning bolt can have a current of 20,000 amperes flowing through it.
  • This current travels through the path offering the least resistance, usually air, which becomes ionized during the strike.
  • Electric current is responsible for the intense heat, light, and sound you see and hear during a lightning storm.
Electric current is key to understanding electricity as it powers our homes, runs our gadgets, and even in spectacular natural phenomena like lightning.
Electron Flow
Electrons are the tiny particles in atoms that, when moving together, create an electric charge.
During a lightning strike, countless electrons flow incredibly quickly between the ground and a storm cloud.
Electrons are essential for an electric charge:
  • The flow of electrons is an integral aspect of electric current.
  • A single electron has a very small charge, specifically about \(1.6 \times 10^{-19}\, \mathrm{C}\).
  • To equate to the charge during lightning, which can be about 2 Coulombs, approximately \(1.25 \times 10^{19}\) electrons must flow during the strike.
This electron movement is not visible to the eye, but the effects are spectacular, as seen in the brilliance of a lightning arc. Understanding electron flow helps to grasp how electric currents operate on such a grand scale during thunderstorms.

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Most popular questions from this chapter

Two charges, one of 2.50\(\mu \mathrm{C}\) and the other of \(-3.50 \mu \mathrm{C}\) , are placed on the \(x\) -axis, one at the origin and the other at \(x=0.600 \mathrm{m}\) , as shown in Fig. 21.36 . Find the position on the \(x\) -axis where the net force on a small charge \(+q\) would be zero. figure can't copy

The ammonia molecule \(\left(\mathrm{NH}_{3}\right)\) has a dipole moment of \(5.0 \times 10^{-30} \mathrm{C} \cdot \mathrm{m} .\) Ammonia molecules in the gas phase are placed in a uniform electric field \(\overrightarrow{\boldsymbol{E}}\) with magnitude \(1.6 \times 10^{6} \mathrm{N} / \mathrm{C}\) . (a) What is the change in electric potential energy when the dipole moment of a molecule changes its orientation with respect to \(\overrightarrow{\boldsymbol{E}}\) from parallel to perpendicular?(b) At what absolute temperature \(\boldsymbol{T}\)is the average translational kinetic energy \(\frac{3}{2} k T\) of a molecule equal to the change in potential energy calculated in part (a)? (Note: Above this temperature, thermal agitation prevents the dipoles from aligning with the electric field.)

A proton is traveling horizontally to the right at \(4.50 \times\) \(10^{6} \mathrm{m} / \mathrm{s}\) (a) Find the magnitude and direction of the weakest electric field that can bring the proton uniformly to rest over a distance of \(3.20 \mathrm{cm} .\) (b) How much time does it take the proton to stop after entering the field? (c) What minimum field (magnitude and direction) would be needed to stop an electron under the conditions of part (a)?

Positive charge \(Q\) is distributed uniformly along the \(x\) -axis from \(x=0\) to \(x=a\) A positive point charge \(q\) is located on the positive \(x\) -axis at \(x=a+r,\) a distance \(r\) to the right of the end of \(Q\) (Fig. 21.47\()\) . (a) Calculate the \(x\) - and \(y\) -components of the electric field produced by the charge distribution \(Q\) at points on the positive \(x\) -axis where \(x>a\) . (b) Calculate the force (magnitnde and direction) that the charge distribution \(Q\) exerts on \(q .\) (c) Show that if \(r \gg a,\) the magnitude of the force in part \((b)\) is approximately \(Q q / 4 \pi \epsilon_{0} r^{2} .\) Explain why this result is obtained.

Infinite sheet \(A\) carries a positive uniform charge density \(\sigma\) , and sheet \(B\) , which is to the right of \(A\) and parallel to it, carries a uniform negative charge density \(-2 \sigma .\) (a) Sketch the electric field lines for this pair of sheets. Include the region between the sheets as well as the regions to the left of \(A\) and to the right of \(B\) . (b) Repeat part (a) for the case in which sheet \(B\) carries a charge density of \(+2 \sigma .\)
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