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Chapter 29

Sources of Magnetic Fields

Magnetic Field due to Moving Charges
Magnetic Field due to Moving Charges
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 ...
Biot-Savart Law
Biot-Savart Law
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 ...
Biot-Savart Law: Problem-Solving
Biot-Savart Law: Problem-Solving
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 ...
Magnetic Field Due To A Thin Straight Wire
Magnetic Field Due To A Thin Straight Wire
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 ...
Magnetic Field Due to Two Straight Wires
Magnetic Field Due to Two Straight Wires
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 Force Between Two Parallel Currents
Magnetic Force Between Two Parallel Currents
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 ...
Magnetic Field Of A Current Loop
Magnetic Field Of A Current Loop
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 ...
Divergence and Curl of Magnetic Field
Divergence and Curl of Magnetic Field
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 ...
Ampere's Law
Ampere's Law
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: Problem-Solving
Ampere's Law: Problem-Solving
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 ...
Solenoids
Solenoids
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 ...
Magnetic Field of a Solenoid
Magnetic Field of a Solenoid
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 ...
Toroids
Toroids
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
Magnetic Vector Potential
In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic ...
Potential Due to a Magnetized Object
Potential Due to a Magnetized Object
Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs ...
Magnetostatic Boundary Conditions
Magnetostatic Boundary Conditions
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
Ampere's Law in Matter
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 ...
Magnetic Susceptibility and Permeability
Magnetic Susceptibility and Permeability
In linear magnetic materials, like paramagnets and diamagnets, magnetization is proportional to the magnetic field intensity. The constant of ...
Magnetic Moment of an Electron
Magnetic Moment of an Electron
Electrons revolving around a nucleus are analogous to a circular current carrying loop. This current produces a magnetic dipole moment proportional to the ...
Diamagnetism
Diamagnetism
Materials consisting of paired electrons have zero net magnetic moments. However, when these materials are placed under an external magnetic field, the ...
Paramagnetism
Paramagnetism
Paramagnets are materials with unpaired electrons that possess a finite magnetic moment. In the absence of a magnetic field, these moments are randomly ...
Ferromagnetism
Ferromagnetism
Materials like iron, nickel, and cobalt consist of magnetic domains, within which the magnetic dipoles are arranged parallel to each other. The magnetic ...
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