Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 28: Problem 10

In a magneto-optic experiment, a liquid sample in a 10 -mL spherical vial is placed in a highly uniform magnetic field, and a laser beam is directed through the sample. Which of the following should be used to create the uniform magnetic field required by the experiment? a) a 5-cm-diameter flat coil consisting of one turn of 4-gauge wire b) a 10 -cm-diameter, 20 turn, single layer, tightly wound coil made of 18 -gauge wire c) a 2 -cm-diameter, 10 -cm long, tightly wound solenoid made of 18 -gauge wire d) a set of two coaxial 10 -cm-diameter coils at a distance of \(5 \mathrm{~cm}\) apart, each consisting of one turn of 4 -gauge wire

Short Answer

Expert verified
Answer: Option D, a set of two coaxial 10-cm-diameter coils, separated by 5 cm, also known as a Helmholtz Coil configuration, will provide the required uniform magnetic field for the magneto-optic experiment.

Step by step solution

01

Identify the factors affecting magnetic field uniformity

The uniformity of the magnetic field is mainly affected by the geometry and current distribution of the coils or solenoids used. Different coil configurations have different levels of uniformity, so we will analyze all the given options - a flat coil, a tightly wound coil, a solenoid, and a set of coaxial coils - and determine which one creates the most uniform magnetic field.
02

Analyze Option A - Flat Coil

A 5-cm-diameter flat coil consisting of one turn of 4-gauge wire would generate a magnetic field following Biot-Savart Law. However, flat coils generally create a non-uniform magnetic field with a significant variation over the area. Because of this, option A is not ideal for creating a highly uniform magnetic field for the experiment.
03

Analyze Option B - Tightly Wound Coil

A 10-cm-diameter, 20 turn, single layer, tightly wound coil made of 18-gauge wire would also generate a magnetic field following Biot-Savart Law. This configuration generally produces a more uniform magnetic field than a flat coil across the central region. However, the field becomes less uniform as we move away from the center. Because the experiment uses a 10-mL spherical vial, this option may not be ideal for covering the whole volume with a highly uniform magnetic field.
04

Analyze Option C - Solenoid

A 2-cm-diameter, 10-cm long, tightly wound solenoid made of 18-gauge wire generates a magnetic field following Ampere's Law. The solenoid configuration is known to produce a highly uniform magnetic field inside its core region. However, the diameter of the solenoid in this case is too small (2 cm) to accommodate the 10-mL spherical vial, which will not allow the sample to be placed inside for the experiment. Therefore, option C is not suitable.
05

Analyze Option D - Coaxial Coils

A set of two coaxial 10-cm-diameter coils at a distance of \(5\mathrm{~cm}\) apart, each consisting of one turn of 4-gauge wire, is known as a Helmholtz Coil configuration. This configuration is specifically designed to create a highly uniform magnetic field in the region between the coils when they are separated by half their diameter (as given in this case). The size of the coils and their separation distance will provide a large enough space for the 10-mL spherical vial and generate the uniform magnetic field required for the experiment.
06

Choose the best option

After analyzing the four options, we can conclude that option D, a set of two coaxial 10-cm-diameter coils, separated by \(5\mathrm{~cm}\), will provide the required uniform magnetic field for the magneto-optic experiment. This Helmholtz Coil configuration will ensure the most uniform field across the volume of the spherical vial and is large enough to accommodate the vial in the experiment setup.

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

In a coaxial cable, the solid core carries a current \(i\) The sheath also carries a current \(i\) but in the opposite direction and has an inner radius \(a\) and an outer radius b. The current density is equally distributed over each conductor. Find an expression for the magnetic field at a distance \(a

A hairpin configuration is formed of two semiinfinite straight wires that are \(2.00 \mathrm{~cm}\) apart and joined by a semicircular piece of wire (whose radius must be \(1.00 \mathrm{~cm}\) and whose center is at the origin of \(x y z\) -coordinates). The top straight wire is along the line \(y=1.00 \mathrm{~cm},\) and the bottom straight wire is along the line \(y=-1.00 \mathrm{~cm} ;\) these two wires are in the left side \((x<0)\) of the \(x y\) -plane. The current in the hairpin is \(3.00 \mathrm{~A},\) and it is directed toward the right in the top wire, clockwise around the semicircle, and to the left in the bottom wire. Find the magnetic field at the origin of the coordinate system.

In a solenoid in which the wires are wound such that each loop touches the adjacent ones, which of the following will increase the magnetic field inside the magnet? a) making the radius of the loops smaller b) increasing the radius of the wire c) increasing the radius of the solenoid d) decreasing the radius of the wire e) immersion of the solenoid in gasoline

The magnetic character of bulk matter is determined largely by electron spin magnetic moments, rather than by orbital dipole moments. (Nuclear contributions are negligible, as the proton's spin magnetic moment is about 658 times smaller than that of the electron.) If the atoms or molecules of a substance have unpaired electron spins, the associated magnetic moments give rise to paramagnetic behavior or to ferromagnetic behavior if the interactions between atoms or molecules are strong enough to align them in domains. If the atoms or molecules have no net unpaired spins, then magnetic perturbations of the electron orbits give rise to diamagnetic behavior. a) Molecular hydrogen gas \(\left(\mathrm{H}_{2}\right)\) is weakly diamagnetic. What does this imply about the spins of the two electrons in the hydrogen molecule? b) What would you expect the magnetic behavior of atomic hydrogen gas (H) to be?

An electron has a spin magnetic moment of magnitude \(\mu=9.285 \cdot 10^{-24} \mathrm{~A} \mathrm{~m}^{2}\). Consequently, it has energy associated with its orientation in a magnetic field. If the difference between the energy of an electron that is "spin up" in a magnetic field of magnitude \(B\) and the energy of one that is "spin down" in the same magnetic field (where "up" and "down" refer to the direction of the magnetic field) is \(9.460 \cdot 10^{-25} \mathrm{~J}\), what is the field magnitude, \(B\) ?
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Waves Physics

Read Explanation

Turning Points in Physics

Read Explanation

Fundamentals of Physics

Read Explanation

Medical Physics

Read Explanation

Kinematics 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.

Sign-up for free