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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.

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Most popular questions from this chapter

Discuss how the accuracy of a compass needle in showing the true direction of north can be affected by the magnetic field due to currents in wires and appliances in a residential building.

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