/*! 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 3 (a) Sketch the electric field li... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 3

(a) Sketch the electric field lines near a point charge \(+q .\) (b) Do the same for a point charge \(-3.00 q\).

Short Answer

Expert verified
For the positive point charge, sketch lines radiating outward. For the negative point charge with magnitude \text{-3.00 q}, sketch more lines converging toward the charge to show a stronger field.

Step by step solution

01

Understanding Electric Field Lines

Electric field lines represent the direction an positive test charge would move if placed in the field. The lines start on positive charges and end on negative charges, representing the direction of the electric force. The density of the lines indicates the strength of the electric field; the closer they are, the stronger the field.
02

Sketching the Electric Field for a Positive Point Charge

To sketch the electric field lines for a positive point charge, draw lines radiating outward from the point charge in all directions. The lines should be evenly spaced and should extend outward indefinitely, since the field of a point charge extends to infinity.
03

Understanding the Electric Field for a Negative Point Charge

For a negative point charge, the electric field lines are directed toward the charge. The magnitude of the point charge affects the number of field lines: a larger magnitude charge will have more lines indicating a stronger field.
04

Sketching the Electric Field for a Negative Point Charge

To sketch the electric field for a negative point charge that is three times as large as the positive charge, draw more lines converging toward the point charge than in Step 2. Ensure that the density of lines reflects that the charge is three times greater to illustrate a stronger electric field.

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!

Key Concepts

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

Electric Charge
Electric charge is a fundamental property of matter that explains how objects experience electromagnetic forces. Charges come in two types: positive and negative. Like charges repel each other, while opposite charges attract. For example, two positive charges will push away from one another, but a positive and a negative charge will pull towards each other.

Everyday materials can become charged in various ways, such as through friction or contact with other charged objects. This is the principle behind static electricity; when you rub a balloon on your hair, it gains electrons from your hair and becomes negatively charged.
Positive and Negative Point Charges
Point charges are idealized charges concentrated at a single point in space. This concept allows us to simplify the complexity of electric fields to one that can be studied and understood more easily. A positive point charge has an excess of protons, while a negative point charge has an excess of electrons.

When visualizing electric field lines, it's important to remember that they emanate outward from a positive point charge. Conversely, for a negative point charge, the lines point inward, indicating that a positive test charge would move toward the negative point charge.
Electric Force
The electric force is a fundamental interaction between charged particles. According to Coulomb's Law, this force is proportional to the product of the charges and inversely proportional to the square of the distance between them. It is conveyed through the electric field, an invisible field around charged particles.

The direction of the electric force is along the line connecting the charges, and its sense depends on whether the charges are like or opposite. In the case of a positive test charge placed near a point charge, the force (and therefore the acceleration of the test charge) is in the direction of the electric field lines that we draw to represent the field.
Field Line Density
Field line density refers to how closely electric field lines are spaced. The field is stronger where the lines are closer together and weaker where they are further apart. This means that if you're looking at a diagram of electric field lines, you can gauge the field's strength by observing the line spacing.

For a positive point charge, the lines will spread out evenly in all directions and the density will decrease as you move further away from the charge. The density of the lines around a negative charge that is three times larger will be significantly greater, reflecting its stronger electric field compared to a smaller charge.

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 test charge of \(+2 \mu \mathrm{C}\) is placed halfway between a charge of \(+6 \mu \mathrm{C}\) and another of \(+4 \mu \mathrm{C}\) separated by \(10 \mathrm{~cm}\). (a) What is the magnitude of the force on the test charge? (b) What is the direction of this force (away from or toward the \(+6 \mu \mathrm{C}\) charge \() ?\)

A certain lightning bolt moves \(40.0 \mathrm{C}\) of charge. How many fundamental units of charge \(\left|q_{e}\right|\) is this?

Body fat is metabolized, supplying 9.30 kcal/g. when dietary intake is less than needed to fuel metabolism. The manufacturers of an exercise bicycle claim that you can lose \(0.500 \mathrm{kg}\) of fat per day by vigorously exercising for \(2.00 \mathrm{h}\) per day on their machine. (a) How many kcal are supplied by the metabolization of \(0.500 \mathrm{kg}\) of fat? (b) Calculate the kcal/min that you would have to utilize to metabolize fat at the rate of \(0.500 \mathrm{kg}\) in \(2.00 \mathrm{h}\). (c) What is unreasonable about the results? (d) Which premise is unreasonable, or which premises are inconsistent?

An electron has an initial velocity of \(5.00 \times 10^{6} \mathrm{~m} / \mathrm{s}\) in a uniform \(2.00 \times 10^{5} \mathrm{~N} / \mathrm{C}\) strength electric field. The field accelerates the electron in the direction opposite to its initial velocity. (a) What is the direction of the electric field? (b) How far does the electron travel before coming to rest? (c) How long does it take the electron to come to rest? (d) What is the electron's velocity when it returns to its starting point?

A shopper pushes a grocery cart \(20.0 \mathrm{m}\) at constant speed on level ground, against a 35.0 N frictional force. He pushes in a direction \(25.0^{\circ}\) below the horizontal. (a) What is the work done on the cart by friction? (b) What is the work done on the cart by the gravitational force? (c) What is the work done on the cart by the shopper? (d) Find the force the shopper exerts, using energy considerations. (e) What is the total work done on the cart?
See all solutions

Recommended explanations on Physics Textbooks

Waves Physics

Read Explanation

Measurements

Read Explanation

Dynamics

Read Explanation

Quantum Physics

Read Explanation

Fields in Physics

Read Explanation

Electricity and Magnetism

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.