Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 17: Problem 66

Before a lightning strike can occur, the breakdown limit for damp air must be reached. If this occurs for an electric field of $3.33 \times 10^{5} \mathrm{V} / \mathrm{m},$ what is the maximum possible height above the Earth for the bottom of a thundercloud, which is at a potential $1.00 \times 10^{8} \mathrm{V}$ below Earth's surface potential, if there is to be a lightning strike?

Short Answer

Expert verified
Answer: Approximately \(300.3 \mathrm{m}\).

Step by step solution

01

Understand the relation between electric field, voltage difference, and distance

An electric field (E) can create a potential difference (V) which is the product of the electric field and the distance (d) between the points. Mathematically, it is given by: \(V = E \times d\) where V is the potential difference, E is the electric field strength, and d is the distance between the points
02

Use given values for electric field and voltage difference

The electric field strength at which the breakdown limit of damp air is reached (E) is given as \(3.33 \times 10^{5} \mathrm{V/m}\). The potential difference between the bottom of the thundercloud and Earth's surface is given as \(1.00 \times 10^{8} \mathrm{V}\).
03

Rearrange the equation to find distance (d)

To find the maximum possible height (d) at which a thundercloud can exist, we can rearrange the equation from step 1 to solve for d, given as: \(d = \frac{V}{E}\) Substitute the values of V and E into the equation: \(d = \frac{1.00 \times 10^{8} \mathrm{V}}{3.33 \times 10^{5} \mathrm{V/m}}\)
04

Calculate the maximum height (d)

Divide the given numbers to find the maximum height: \(d = \frac{1.00 \times 10^{8}}{3.33 \times 10^{5}}\) \(d = 300.3 \mathrm{m}\) So, the maximum possible height above the Earth for the bottom of a thundercloud, which is at a potential \(1.00 \times 10^{8} \mathrm{V}\) below Earth's surface potential, to have a lightning strike is approximately \(300.3 \mathrm{m}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A van de Graaff generator has a metal sphere of radius \(15 \mathrm{cm} .\) To what potential can it be charged before the electric field at its surface exceeds \(3.0 \times 10^{6} \mathrm{N} / \mathrm{C}\) (which is sufficient to break down dry air and initiate a spark)?
An alpha particle (helium nucleus, charge \(+2 e\) ) starts from rest and travels a distance of \(1.0 \mathrm{cm}\) under the influence of a uniform electric field of magnitude \(10.0 \mathrm{kV} / \mathrm{m}\) What is the final kinetic energy of the alpha particle?
Find the electric potential energy for the following array of charges: charge \(q_{1}=+4.0 \mu \mathrm{C}\) is located at \((x, y)=(0.0,0.0) \mathrm{m} ;\) charge \(q_{2}=+3.0 \mu \mathrm{C}\) is located at \((4.0,3.0) \mathrm{m} ;\) and charge \(q_{3}=-1.0 \mu \mathrm{C}\) is located at (0.0,3.0) \(\mathrm{m}\)
It is believed that a large electric fish known as Torpedo occidentalis uses electricity to shock its victims. A typical fish can deliver a potential difference of \(0.20 \mathrm{kV}\) for a duration of \(1.5 \mathrm{ms}\). This pulse delivers charge at a rate of \(18 \mathrm{C} / \mathrm{s} .\) (a) What is the rate at which work is done by the electric organs during a pulse? (b) What is the total amount of work done during one pulse?
A positively charged oil drop is injected into a region of uniform electric field between two oppositely charged, horizontally oriented plates spaced $16 \mathrm{cm}$ apart. If the mass of the drop is \(1.0 \times 10^{-13} \mathrm{kg}\) and it remains stationary when the potential difference between the plates is $9.76 \mathrm{kV},$ what is the magnitude of the charge on the drop? (Ignore the small buoyant force on the drop.)
See all solutions

Recommended explanations on Physics Textbooks

Radiation

Read Explanation

Energy Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Nuclear Physics

Read Explanation

Electromagnetism

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free