Chapter 29
Sources of Magnetic Fields
Chapter 29
Sources of Magnetic Fields
A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a …
The Biot-Savart law gives the magnitude and direction of the magnetic field produced by a current. This empirical law was named in honor of two …
The magnitude and direction of a magnetic field created by a steady current can be calculated using the Biot-Savart law.
Consider a mobile phone battery …
Consider an infinitely long straight wire carrying a current I. The magnetic field at point P at a distance a from the origin can be calculated using the …
Consider two parallel straight wires carrying a current of 10 A and 20 A in the same direction and separated by a distance of 20 cm. Calculate the …
Two long, straight, and parallel current-carrying conductors exert a force of equal magnitude on one another. The direction of the force depends on the …
Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the …
The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
To evaluate the divergence of the …
A fundamental property of a static magnetic field is that it is not conservative, unlike an electrostatic field. Instead, there is a relationship between …
Ampere's law states that for any closed looped path, the line integral of the magnetic field along the path equals the vacuum permeability times the …
A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field for a solenoid is the …
A solenoid is a conducting wire coated with an insulating material, wound tightly in the form of a helical coil. The magnetic field due to a solenoid is …
A toroid is a closely wound donut-shaped coil constructed using a single conducting wire. In general, it is assumed that a toriod consists of …
In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic …
Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs …
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular …
The total current density in magnetized material is the sum of the free and bound current densities. The free current arises due to the motion of free …
In linear magnetic materials, like paramagnets and diamagnets, magnetization is proportional to the magnetic field intensity. The constant of …
Electrons revolving around a nucleus are analogous to a circular current carrying loop. This current produces a magnetic dipole moment proportional to the …
Materials consisting of paired electrons have zero net magnetic moments. However, when these materials are placed under an external magnetic field, the …
Paramagnets are materials with unpaired electrons that possess a finite magnetic moment. In the absence of a magnetic field, these moments are randomly …
Materials like iron, nickel, and cobalt consist of magnetic domains, within which the magnetic dipoles are arranged parallel to each other. The magnetic …
The aortic valve, located between the left ventricle and the aorta, allows for unidirectional blood flow, preventing backflow into the ventricle. Aortic …
While the first Electron Paramagnetic Resonance (EPR) studies regarding the effects of oxidation on the structure and stability of carbon radicals date …
The accurate and specific detection of reactive oxygen species (ROS) in different cellular and tissue compartments is essential to the study of …
Thickness quantification of conductive ferromagnetic materials by means of non-destructive evaluation (NDE) is a crucial component of structural health …