/*! 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 2 1 lies on the \(x\) -axis and it... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 19: Problem 2

1 lies on the \(x\) -axis and its north end is at \(x=+1.0 \mathrm{~cm},\) while its s鈥� # Two identical bar magnets of negligible width are located in the \(x\) -y plane. Magnet #1 lies on the \(x\) -axis and its north end is at \(x=+1.0 \mathrm{~cm},\) while its south end is at \(x=+5.0 \mathrm{~cm}\). Magnet #2 lies on the \(y\) -axis and its north end is at \(y=+1.0 \mathrm{~cm},\) while its south end is at \(y=+5.0 \mathrm{~cm} .\) (a) In what direction would a compass point if it were located at the origin? (b) Repeat part (a) for the situation where magnet #1 is reversed in polarity. [Hint: Make a sketch of the two magnets and their individual fields at the origin.

Short Answer

Expert verified
(a) Northeast; (b) Northwest.

Step by step solution

01

Analyze Magnet #1

Magnet #1 lies on the x-axis from \(x=+1.0\, \text{cm}\) to \(x=+5.0\, \text{cm}\). Its north pole is at \(x=+1.0\, \text{cm}\), and its south pole is at \(x=+5.0\, \text{cm}\). Therefore, the direction of the magnetic field at the origin (\(x=0\)) due to Magnet #1 would point from the north pole towards the south pole along the x-axis, which means the magnetic field direction is towards the positive x-direction.
02

Analyze Magnet #2

Magnet #2 lies on the y-axis with its north end at \(y=+1.0\, \text{cm}\) and its south end at \(y=+5.0\, \text{cm}\). At the origin, the magnetic field direction due to Magnet #2 would point from its north pole towards its south pole along the y-axis, leading the magnetic field to point towards the positive y-direction.
03

Determine Net Magnetic Field Direction at Origin for Part (a)

At the origin, Magnet #1 creates a magnetic field pointing in the positive x-direction, while Magnet #2 creates a magnetic field pointing in the positive y-direction. These fields are perpendicular to each other, so the resultant direction can be found by vector addition. The net magnetic field would result in a direction towards the northeast (a 45掳 angle between the positive x and y axes).
04

Determine Net Magnetic Field Direction for Part (b)

For part (b), where Magnet #1's polarity is reversed, the north pole is now at \(x=+5.0\, \text{cm}\) and the south pole at \(x=+1.0\, \text{cm}\). The magnetic field at the origin for Magnet #1 now points from the south to the north, resulting in a direction towards the negative x-direction. Combining this with the magnetic field from Magnet #2 (still pointing in the positive y-direction), the net magnetic field points towards the northwest (a 135掳 angle between the negative x and positive y axes).

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.

Bar Magnets
Bar magnets are fascinating objects that produce a magnetic field, each with a specific orientation. They have two poles: a north and a south pole. The magnetic field direction always runs from the north pole to the south pole outside the magnet. This orientation affects how they interact with other magnets and magnetic materials.
  • Poles: A bar magnet has clearly defined north and south poles.
  • Magnetic Field Lines: The lines emanate from the north pole and loop back to enter the south pole.
  • Magnetic Interaction: Two magnets can attract or repel each other depending on their pole interactions.
Bar magnets are commonly used in compasses and have applications in many devices that rely on Earth's magnetic field.
Compass Direction
A compass is a simple yet effective tool that uses a freely pivoting magnetized needle to indicate direction relative to Earth's magnetic poles. The needle aligns itself along the magnetic field lines, pointing towards the magnetic north.
  • Utilization: Compasses help navigate by aligning with Earth's magnetic field.
  • Principles: Compasses exploit the magnetic field generated by bar magnets.
  • Influence of Nearby Magnets: The presence of other magnets can alter the compass needle direction due to their local magnetic fields.
In our exercise, the compass at the origin is affected by both bar magnets, with one magnet on the x-axis and the other on the y-axis.
Magnetic Polarity
Magnetic polarity is crucial in understanding how bar magnets work. Each magnet has two poles: north and south. These poles dictate the direction and strength of a magnet's field.
  • North and South: The north pole of one magnet will seek the south pole of another.
  • Field Direction: Field lines are drawn from north to south outside of the magnet.
  • Reversal Impact: Switching a magnet's polarity changes how it interacts with other fields.
In exercises involving multiple magnets, as with the reversed polarity in part (b), the interaction and field directions change, impacting the compass direction observed.
Vector Addition
Vector addition is a mathematical operation used to find the resultant direction and magnitude when combining multiple vectors. Each vector has a magnitude and direction.
  • Addition Method: Vectors can be added graphically using the head-to-tail method to determine the resultant vector.
  • Application: This is essential in physics problems where multiple forces or fields influence an object.
  • Perpendicular Vectors: The resultant of two perpendicular vectors can be found using the Pythagorean theorem.
In the problem, vector addition helps calculate the effective magnetic field direction at the origin by combining the fields from the two perpendicular magnets.
X-Y Plane
The x-y plane is a flat, two-dimensional surface used in mathematics and physics to describe positions and movements.
  • Coordinate System: Points are described with a coordinate pair (x, y).
  • Perpendicular Axes: The plane comprises two perpendicular lines, the x-axis and the y-axis.
  • Applications: Many physical problems are simplified when analyzed in the x-y plane.
In our exercise, the magnets lie along the x and y axes, creating fields that must be understood within this framework to determine the compass needle's direction.

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) What angle(s) does a particle's velocity have to make with the magnetic field direction for the particle to be subjected to half the maximum possible magnetic force, \(F_{\max } ?\) (b) Express the magnetic force on a charged particle in terms of \(F_{\max }\) if the angle between its velocity and the magnetic field direction is (i) \(10^{\circ},\) (ii) \(80^{\circ},\) and (iii) \(100^{\circ} .\) (c) If the particle's velocity makes an angle of \(50^{\circ}\) with respect to the magnetic field direction, at what other angle(s) would the magnetic force on it be the same? Would the direction be the same? Explain.

A positive charge moves horizontally to the right across this page and enters a magnetic field directed vertically downward in the plane of the page. (a) What is the direction of the magnetic force on the charge: (1) into the page, (2) out of the page, (3) downward in the plane of the page, or (4) upward in the plane of the page? Explain. (b) If the charge is \(0.25 \mathrm{C}\), its speed is \(2.0 \times 10^{2} \mathrm{~m} / \mathrm{s},\) and it is acted on by a force of \(20 \mathrm{~N},\) what is the magnetic field strength?

What is the (a) "current" due to the electron orbiting in a circular path about the proton in a hydrogen atom? (b) What magnetic field strength does this "electron current" create at the proton location? (c) If the electron is orbiting clockwise, as viewed from above its orbital plane, what is the direction of this field? Take the orbital radius to be \(0.0529 \mathrm{nm}\). [Hint: Find the electron's period by considering the centripetal force.]

A circular wire coil consists of 100 turns and is wound tightly around a very long iron cylinder with a radius of \(2.5 \mathrm{~cm}\) and a relative permeability of \(2200 .\) The loop has a current of \(7.5 \mathrm{~A}\) in it. Determine the magnetic field strength produced by the coil (a) at the center of the coil and (b) at a location on the central axis of the iron cylinder \(5.0 \mathrm{~cm}\) above the center of the circular coil.

A charged particle travels undeflected through perpendicular electric and magnetic fields whose magnitudes are \(3000 \mathrm{~N} / \mathrm{C}\) and \(30 \mathrm{mT}\), respectively. Find the speed of the particle if it is (a) a proton and (b) an alpha particle. (An alpha particle is a helium nucleus-a positive ion with a double positive charge of \(+2 e .\) )
See all solutions

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Read Explanation

Translational Dynamics

Read Explanation

Engineering Physics

Read Explanation

Scientific Method Physics

Read Explanation

Quantum Physics

Read Explanation

Waves 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.