Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 1619

Iaking earth to be a metallic spheres, its capacity will approximately be (A) \(6.4 \times 10^{6} \mathrm{~F}\) (B) \(700 \mathrm{pF}\) (C) \(711 \mu \mathrm{F}\) (D) \(700 \mathrm{pF}\)

Short Answer

Expert verified
The capacitance of Earth, considering it to be a metallic sphere, can be calculated using the formula \(C = 4 \pi \varepsilon_0 R\), where \(\varepsilon_0\) is the permittivity of free space and \(R\) is the radius of Earth. Plugging in the values \(\varepsilon_0 \approx 8.85 \times 10^{-12} \mathrm{F/m}\) and \(R \approx 6.37 \times 10^6 \mathrm{m}\), we get \(C \approx 712.49 \times 10^{-6} \mathrm{F}\). Comparing this to the given options, the closest value is (C) \(711 \mu \mathrm{F}\), which is the correct answer.

Step by step solution

01

Insert the values into the formula

Now we will insert the values \(\varepsilon_0\) and \(R\) into the capacitance formula: \[C = 4 \pi (8.85 \times 10^{-12} \mathrm{F/m}) (6.37 \times 10^6 \mathrm{m})\]
02

Solve for capacitance

To solve for capacitance, we just need to do the arithmetic: \[C = 4 \pi(8.85 \times 10^{-12} \mathrm{F/m}) (6.37 \times 10^6 \mathrm{m})\] \[C = 4 \pi(56.4855 \times 10^{-6} \mathrm{F})\] Next, we multiply the values: \[C = 4 \pi(56.4855 \times 10^{-6} \mathrm{F}) \approx 712.49 \times 10^{-6} \mathrm{F}\]
03

Choose the correct option

The calculated value of Earth's capacitance is approximately \(712.49 \mu \mathrm{F}\). Comparing the calculated value to the given options, we find that option (C) \(711 \mu \mathrm{F}\) is the closest to our result. Hence, the answer is: (C) \(711 \mu \mathrm{F}\)

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

Two positive point charges of \(12 \mu \mathrm{c}\) and \(8 \mu \mathrm{c}\) are placed \(10 \mathrm{~cm}\) apart in air. The work done to bring them $4 \mathrm{~cm}$ closer is (A) Zero (B) \(4.8 \mathrm{~J}\) (C) \(3.5 \mathrm{~J}\) (D) \(-5.8 \mathrm{~J}\)

If 3 charges are placed at the vertices of equilateral triangle of charge ' \(q\) ' each. What is the net potential energy, if the side of equilateral triangle is \(\ell \mathrm{cm}\). (A) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(3 q^{2} / \ell\right)$ (B) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(2 q^{2} / \ell\right)$ (C) \(\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(q^{2} / \ell\right)\) (D) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(4 q^{2} / \ell\right)$

An electrical technician requires a capacitance of \(2 \mu \mathrm{F}\) in a circuit across a potential difference of \(1 \mathrm{KV}\). A large number of $1 \mu \mathrm{F}$ capacitors are available to him, each of which can withstand a potential difference of not than \(400 \mathrm{~V}\). suggest a possible arrangement that requires a minimum number of capacitors. (A) 2 rows with 2 capacitors (B) 4 rows with 2 capacitors (C) 3 rows with 4 capacitors (D) 6 rows with 3 capacitors

Large number of capacitors of rating $10 \mu \mathrm{F} / 200 \mathrm{~V} \mathrm{~V}$ are available. The minimum number of capacitors required to design a \(10 \mu \mathrm{F} / 700 \mathrm{~V}\) capacitor is (A) 16 (B) 8 (C) 4 (D) 7

Charges of \(+(10 / 3) \times 10^{-9} \mathrm{C}\) are placed at each of the four corners of a square of side \(8 \mathrm{~cm}\). The potential at the intersection of the diagonals is ...... (A) \(150 \sqrt{2}\) Volt (B) \(900 \sqrt{2}\) Volt (C) \(1500 \sqrt{2}\) Volt (D) \(900 \sqrt{2} \cdot \sqrt{2}\) Volt
See all solutions

Recommended explanations on English Textbooks

Morphology

Read Explanation

Text Comparison

Read Explanation

Phonetics

Read Explanation

Graphology

Read Explanation

Textual Analysis

Read Explanation

English Language Study

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