Chapter 29
Sources of Magnetic Fields
![Magnetic Field due to Moving Charges](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/14089.jpg)
A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving…
![Biot-Savart Law](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/13773.jpg)
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…
![Magnetic Field Due To A Thin Straight Wire](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/13775.jpg)
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…
![Magnetic Field Due to Two Straight Wires](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/14198.jpg)
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…
![Magnetic Field Of A Current Loop](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/13777.jpg)
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…
![Divergence and Curl of Magnetic Field](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/14199.jpg)
The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
To evaluate the divergence…
![Ampere's Law: Problem-Solving](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/13779.jpg)
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…
![Solenoids](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/13780.jpg)
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…
![Toroids](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/13781.jpg)
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…
![Magnetic Vector Potential](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/14204.jpg)
In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the…
![Magnetostatic Boundary Conditions](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/14202.jpg)
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular…
![Ampere's Law in Matter](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/14201.jpg)
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…
![Magnetic Moment of an Electron](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/13782.jpg)
Electrons revolving around a nucleus are analogous to a circular current carrying loop. This current produces a magnetic dipole moment proportional…
![Diamagnetism](https://cloudfront.jove.com/files/media/science-education/science-education-thumbs/13783.jpg)
Materials consisting of paired electrons have zero net magnetic moments. However, when these materials are placed under an external magnetic field,…
![Design of a Cyclic Pressure Bioreactor for the <em>Ex Vivo</em> Study of Aortic Heart Valves](https://cloudfront.jove.com/files/thumbs/3316_t.png)
The aortic valve, located between the left ventricle and the aorta, allows for unidirectional blood flow, preventing backflow into the ventricle.…
![Exploring the Radical Nature of a Carbon Surface by Electron Paramagnetic Resonance and a Calibrated Gas Flow](https://cloudfront.jove.com/files/thumbs/51548_t.png)
While the first Electron Paramagnetic Resonance (EPR) studies regarding the effects of oxidation on the structure and stability of carbon radicals…