A toroidal solenoid with 400 turns of wire and a mean radius...

Name: Problem 52, Chapter 28: University Physics with Modern Physics
Uploaded: 2019-04-29T04:31:40-08:00
Duration: 3 min 28 s
Channel: Carolyn Shasha
Description: A toroidal solenoid with 400 turns of wire and a mean radius of 6.0 cm carries a current of 0.25 A. The relative permeability of the core is 80. (a) What is the magnetic field in the core? (b) What part of the magnetic field is due to atomic currents?

A toroidal solenoid with 400 turns of wire and a mean radius of 6.0 cm carries a current of 0.25 A. The relative permeability of the core is 80. (a) What is the magnetic field in the core? (b) What part of the magnetic field is due to atomic currents?

Key Concepts

Relative Permeability

Relative permeability is a measure of how much a material can become magnetized in response to an applied magnetic field compared to free space. It is defined as the ratio of the permeability of the material to the permeability of free space. In a toroidal solenoid with a magnetic core, the relative permeability amplifies the magnetic field produced by the current in the wire turns, resulting in a stronger overall magnetic field within the core.

Toroidal Solenoid

A toroidal solenoid is a coil of wire wound in the shape of a torus (a donut). In this configuration, the magnetic field is largely confined within the core of the toroid, which minimizes external magnetic fields and losses. This geometry is widely used in applications where a well-contained magnetic field is desired.

Ampere's Law

Ampere’s Law is a fundamental principle in electromagnetism that relates the magnetic field circulating around a closed path to the electric current passing through that path. In the context of a toroidal solenoid, it is used to derive the expression for the magnetic field inside the core by integrating the field along a circular path located within the solenoid.

Atomic Currents

Atomic currents refer to the microscopic loops of current arising from the motion of electrons in atoms, which contribute to the magnetic properties of materials. In magnetic materials, these atomic or bound currents are responsible for the intrinsic magnetization. When an external magnetic field is applied, these contributions align with the field and add to the overall magnetic flux in the material. Distinguishing the field produced by the free currents (from the windings) and that due to the atomic currents (intrinsic material response) is important for understanding the magnetic behavior of the core.

Transcript

Please give Ace some feedback