/*! 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 60 Imagine a long straight wire per... [FREE SOLUTION] | 91Ó°ÊÓ

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Imagine a long straight wire perpendicular to the page and carrying a current \(I\) into the page. Sketch some \(\overrightarrow{\mathbf{B}}\) field lines with arrowheads to indicate directions.

Short Answer

Expert verified
The magnetic field lines form concentric circles around the wire, flowing counterclockwise.

Step by step solution

01

Understand the Right-Hand Rule

The right-hand rule helps us determine the direction of the magnetic field around a current-carrying wire. Imagine grasping the wire with your right hand, with your thumb pointing in the direction of the current. Your curled fingers will then point in the direction of the magnetic field lines.
02

Apply the Right-Hand Rule

For a current flowing into the page, envision your thumb directed straight into the page. Your fingers should curl around the wire, moving in a counterclockwise direction around the point where the wire penetrates the paper. This shows the path and direction of the magnetic field.
03

Draw Magnetic Field Lines

Using the information from the right-hand rule, draw concentric circles around the point representing the wire on the page. These circles move in a counterclockwise direction when viewed from above the page.
04

Add Arrowheads to Indicate Direction

Attach arrowheads to the drawn circles, pointing counterclockwise. This visually indicates that the magnetic field lines are circulating counterclockwise as the current enters the page.

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Key Concepts

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

Right-Hand Rule
In physics, the right-hand rule is a useful tool for understanding the direction of a magnetic field when dealing with a current-carrying wire. This rule is quite intuitive and straightforward. Imagine you are holding the wire in your right hand. Your thumb must point in the direction of the electric current, which is crucial for visualizing the magnetic field. Once your thumb is pointing correctly, your fingers naturally curl around the wire. This curling motion of your fingers represents the direction in which the magnetic field is oriented.

Remember, this rule applies universally, but you must use your right hand specifically. If you try it with your left hand, you'll actually get the reverse direction, which can lead to confusion. This simple hand gesture allows you to visualize the magnetic field lines surrounding a current-carrying wire in a clear and practical way.
Current-Carrying Wire
A current-carrying wire is a fundamental component in electrical circuits and physics. When electricity, or current, flows through a wire, it generates a magnetic field around it. This phenomenon is due to the movement of electric charges, providing the wire with its magnetic quality.

A common model involves a long straight wire; this is generally easier to analyze mathematically and conceptually. The current direction is particularly vital because it influences the orientation of the magnetic field around the wire. The current flowing into or out of the page alters the way the magnetic field lines are oriented, as depicted by using the right-hand rule.

In practical terms, these wires are vital in countless electrical applications, from simple circuits to complex, large-scale electromagnets. Understanding the behavior of the magnetic field around these wires allows for effective design and use of electronic devices and components.
Magnetic Field Lines
Magnetic field lines are visual representations of the magnetic field's direction and strength surrounding an object, such as a current-carrying wire. These lines run in continuous loops from the north pole to the south pole outside a magnet, or form concentric circles around a wire, as the exercise illustrates.

When sketching these lines around a wire, remember the influence of the right-hand rule. If the current is directed into the page, the magnetic field lines form concentric circles around the wire, moving in a counterclockwise direction when viewed from above.

The density of these lines gives us insights into the field's strength; more lines indicate a stronger field closer to the wire. By adding arrowheads to these drawn lines, you communicate the direction of the field, providing a comprehensive visual model. This approach is widely used to help individuals visualize and understand the dynamic nature of magnetic fields in a clear and accessible manner.

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Most popular questions from this chapter

An electromagnetic flowmeter is to be used to measure blood speed. A magnetic field of \(0.115 \mathrm{T}\) is applied across an artery of inner diameter \(3.80 \mathrm{mm}\) The Hall voltage is measured to be \(88.0 \mu \mathrm{V} .\) What is the average speed of the blood flowing in the artery?
Two identical bar magnets lie next to one another on a table. Sketch the magnetic field lines if the north poles are at opposite ends.
An early cyclotron at Cornell University was used from the 1930 s to the 1950 s to accelerate protons, which would then bombard various nuclei. The cyclotron used a large electromagnet with an iron yoke to produce a uniform magnetic field of \(1.3 \mathrm{T}\) over a region in the shape of a flat cylinder. Two hollow copper dees of inside radius \(16 \mathrm{cm}\) were located in a vacuum chamber in this region. (a) What is the frequency of oscillation necessary for the alternating voltage difference between the dees? (b) What is the kinetic energy of a proton by the time it reaches the outside of the dees? (c) What would be the equivalent voltage necessary to accelerate protons to this energy from rest in one step (say between parallel plates)? (d) If the potential difference between the dees has a magnitude of $10.0 \mathrm{kV}$ each time the protons cross the gap, what is the minimum number of revolutions each proton has to make in the cyclotron?
A singly charged ion of unknown mass moves in a circle of radius $12.5 \mathrm{cm}\( in a magnetic field of \)1.2 \mathrm{T}$. The ion was accelerated through a potential difference of \(7.0 \mathrm{kV}\) before it entered the magnetic field. What is the mass of the ion?
Electrons in a television's CRT are accelerated from rest by an electric field through a potential difference of \(2.5 \mathrm{kV} .\) In contrast to an oscilloscope, where the electron beam is deflected by an electric ficld, the beam is deflected by a magnetic field. (a) What is the specd of the electrons? (b) The beam is deflected by a perpendicular magnetic field of magnitude $0.80 \mathrm{T}$. What is the magnitude of the acceleration of the electrons while in the field? (c) What is the speed of the electrons after they travel 4.0 mm through the magnetic field? (d) What strength electric field would give the electrons the same magnitude acceleration as in (b)? (c) Why do we have to use an clectric ficld in the first place to get the electrons up to speed? Why not use the large acceleration due to a magnetic field for that purpose?
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