Question

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

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

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.

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.

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.

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.

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.

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.

Key concepts

Uniform Magnetic Field

A uniform magnetic field is a consistent magnetic field that remains the same in strength and direction over the specified area or volume. This uniformity is crucial in many scientific experiments, particularly those involving magneto-optics, because any variation in the field can lead to uneven effects on the sample.
In the context of the given experiment, the goal is to maintain a constant magnetic influence across the entire liquid sample. This ensures that measurements taken are accurate and reflect the sample's true properties, without interference from field inconsistencies.
Achieving a uniform magnetic field can be challenging because many factors can introduce irregularities. The choice of equipment and the arrangement of coils greatly impact the uniformity achieved. This is why, in magneto-optic experiments, it is essential to select the right configuration to provide a truly uniform field.

Helmholtz Coils

Helmholtz coils are a specific arrangement of two identical circular magnetic coils that are spaced apart, typically by a distance equal to the radius of the coils. This setup is designed to generate a highly uniform magnetic field in the region between the coils.

• The Helmholtz coil configuration is particularly useful in experiments where field uniformity is critical because it minimizes variations in the magnetic field in the central area.
• By carefully positioning the coils at a distance equal to their radius, the field produced cancels out non-uniformities found in simpler coil designs.
• In the provided exercise, this coil setup (option D) is noted as the optimal choice because it can generate the desired uniform field needed for the experiment.

Helmholtz coils are excellent for offering a balance between simplicity and performance, making them a common choice in many magnetic field applications.

Coil Configurations

The setup or configuration of coils significantly influences the type of magnetic field produced. Different arrangements can result in varying degrees of field uniformity and coverage.
Common configurations include:

• Flat Coils: These produce fields with significant variation and are not typically used where uniformity is critical.
• Tightly Wound Coils: Such coils can offer uniform fields but may struggle with uniformity over larger volumes unless specifically designed like solenoids.
• Solenoids: They can give a highly uniform field inside their core. However, their typically small diameter can limit the volume they can accommodate, as highlighted by the constraints in option C.
• Coaxial Coils: As in the Helmholtz configuration, they provide excellent uniformity between the coils when spaced correctly.

The choice of coil configuration should align with the needs of the experiment, focusing on ensuring that the magnetic field remains consistent across the target area.

Magnetic Field Analysis

Magnetic field analysis involves assessing how different configurations impact the uniformity and strength of a magnetic field. This analysis is crucial for understanding which setup will provide the best results in an experiment.
In the experiment under discussion, analyzing the magnetic characteristics of each coil option led to the conclusion that the Helmholtz coil configuration (option D) was superior. This choice was based on its proven ability to maintain field uniformity over the required area.
Effective magnetic field analysis considers several factors:

• The geometry and arrangement of the coils, which directly impact field uniformity.
• The current distribution and strength, as they define the path and consistency of the magnetic field lines.
• Practical constraints, such as the size of the experimental setup and the specific requirements of the sample being studied.

Utilizing such an analysis ensures that experiments are planned with precision, minimizing errors due to magnetic field irregularities.