/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 29 What are the magnitude and direc... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 16: Problem 29

What are the magnitude and direction of the electric field midway between two point charges, \(-15 \mu \mathrm{C}\) and \(+12 \mu \mathrm{C},\) that are $8.0 \mathrm{cm}$ apart?

Short Answer

Expert verified
Answer: To find the magnitude and direction of the electric field midway between the point charges, follow these steps: 1. Determine the position of the midpoint: The midpoint is located at 4 cm from each charge. 2. Calculate the electric field due to each charge using the electric field formula, and find the values for E1 and E2. 3. Determine the net electric field at the midpoint: E_net = |E1 - E2|. 4. Determine the direction of the net electric field, which points towards the -15 渭C charge, as it has a larger magnitude. Using the given values and formula, you can calculate the magnitude of the electric field and find that the direction is towards the -15 渭C charge.

Step by step solution

01

Determine the Position of the Midpoint

To find the position of the midpoint, we'll take the average of the distances of the two charges. Since the charges are 8 cm apart, the midpoint is located at 4 cm from each charge.
02

Calculate the Electric Field due to Each Charge

Use the formula for the electric field of a point charge: \(E = k\frac{|q|}{r^2}\), where \(k = 8.9875 \times 10^9 \mathrm{N\cdot m^2 \cdot C^{-2}}\) is the electrostatic constant, q is the charge, and r is the distance between the charge and the midpoint. For the \(-15 \mu C\) charge: \(E_1 = k\frac{|-15 \times 10^{-6} C|}{(0.04 m)^2}\) For the \(+12 \mu C\) charge: \(E_2 = k\frac{12 \times 10^{-6} C}{(0.04 m)^2}\) Calculate the values for \(E_1\) and \(E_2\).
03

Determine the Net Electric Field at the Midpoint

Since the electric fields of the two charges have opposite directions, the net electric field is the difference between their magnitudes: \(E_{net} = |E_1 - E_2|\) Calculate the value for \(E_{net}\).
04

Determine the Direction of the Net Electric Field

The direction of the net electric field depends on which charge has a larger magnitude. In this case, the \(-15 \mu C\) charge has a larger magnitude, so the net electric field will point towards this charge. The magnitude and direction of the electric field midway between the two point charges are found by following these steps.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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 point charge \(q_{1}=+5.0 \mu \mathrm{C}\) is fixed in place at \(x=0\) and a point charge \(q_{2}=-3.0 \mu \mathrm{C}\) is fixed at \(x=\) $-20.0 \mathrm{cm} .\( Where can we place a point charge \)q_{3}=-8.0 \mu \mathrm{C}$ so that the net electric force on \(q_{1}\) due to \(q_{2}\) and \(q_{3}\) is zero?
\(\mathrm{A}+2.0\) -nC point charge is \(3.0 \mathrm{cm}\) away from a $-3.0 \mathrm{-nC}$ point charge. (a) What are the magnitude and direction of the electric force acting on the +2.0 -nC charge? (b) What are the magnitude and direction of the electric force acting on the -3.0 -nC charge?

A metal sphere A has charge \(Q\). Two other spheres, B and \(\mathrm{C},\) are identical to \(\mathrm{A}\) except they have zero net charge. A touches \(\mathrm{B}\), then the two spheres are separated. B touches \(C\), then those spheres are separated. Finally, C touches A and those two spheres are separated. How much charge is on each sphere?
A balloon, initially neutral, is rubbed with fur until it acquires a net charge of \(-0.60 \mathrm{nC} .\) (a) Assuming that only electrons are transferred, were electrons removed from the balloon or added to it? (b) How many electrons were transferred?
In this problem, you can show from Coulomb's law that the constant of proportionality in Gauss's law must be \(1 / \epsilon_{0} .\) Imagine a sphere with its center at a point charge q. (a) Write an expression for the electric flux in terms of the field strength \(E\) and the radius \(r\) of the sphere. [Hint: The field strength \(E\) is the same everywhere on the sphere and the field lines cross the sphere perpendicular to its surface.] (b) Use Gauss's law in the form \(\Phi_{\mathrm{E}}=c q(\text { where } c\) is the constant of proportionality) and the electric field strength given by Coulomb's law to show that $c=1 / \epsilon_{0}$
See all solutions

Recommended explanations on Physics Textbooks

Magnetism

Read Explanation

Electricity

Read Explanation

Famous Physicists

Read Explanation

Medical Physics

Read Explanation

Mechanics and Materials

Read Explanation

Space 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.