Chapter 5 Overview. Electric vs Magnetic Comparison.
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Transcript of Chapter 5 Overview. Electric vs Magnetic Comparison.
![Page 1: Chapter 5 Overview. Electric vs Magnetic Comparison.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e5d5503460f94b56a6f/html5/thumbnails/1.jpg)
Chapter 5 Overview
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Electric vs Magnetic Comparison
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Electric & Magnetic Forces
Electromagnetic (Lorentz) force
Magnetic force
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Magnetic Force on a Current Element
Differential force dFm on a differential current I dl:
![Page 5: Chapter 5 Overview. Electric vs Magnetic Comparison.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e5d5503460f94b56a6f/html5/thumbnails/5.jpg)
Torque
d = moment armF = forceT = torque
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Magnetic Torque on Current Loop
No forces on arms 2 and 4 ( because I and B are parallel, or anti-parallel)
Magnetic torque:
Area of Loop
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Inclined Loop
For a loop with N turns and whose surface normal is at angle that relative to B direction:
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Biot-Savart Law
Magnetic field induced by a differential current:
For the entire length:
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Magnetic Field due to Current Densities
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Example 5-2: Magnetic Field of Linear Conductor
Cont.
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Example 5-2: Magnetic Field of Linear Conductor
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Magnetic Field of Long Conductor
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Example 5-3: Magnetic Field of a Loop
Cont.
dH is in the r–z plane , and therefore it hascomponents dHr and dHz
z-components of the magnetic fields due to dl and dl’ add because they are in the same direction, but their r-components cancel
Hence for element dl:
Magnitude of field due to dl is
![Page 14: Chapter 5 Overview. Electric vs Magnetic Comparison.](https://reader035.fdocuments.in/reader035/viewer/2022062314/56649e5d5503460f94b56a6f/html5/thumbnails/14.jpg)
Example 5-3:Magnetic Field of a Loop (cont.)
For the entire loop:
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Magnetic Dipole
Because a circular loop exhibits a magnetic field pattern similar to the electric field of an electric dipole, it is called a magnetic dipole
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Forces on Parallel Conductors
Parallel wires attract if their currents are in the same direction, and repel if currents are in opposite directions
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Ampère’s Law
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Internal Magnetic Field of Long ConductorFor r < a
Cont.
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External Magnetic Field of Long Conductor
For r > a
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Magnetic Field of Toroid
Applying Ampere’s law over contour C:
The magnetic field outside the toroid is zero. Why?
Ampere’s law states that the line integral of H around a closed contour C is equal to the current traversing the surface bounded by the contour.
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Magnetic Vector Potential A
Electrostatics
Magnetostatics
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Magnetic Properties of Materials
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Magnetic Hysteresis
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Boundary Conditions
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Solenoid
Inside the solenoid:
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Inductance
Magnetic Flux
Flux Linkage
Inductance
Solenoid
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The magnetic field in the region S between the two conductors is approximately
Example 5-7: Inductance of Coaxial Cable
Total magnetic flux through S:
Inductance per unit length:
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Magnetic Energy Density
Magnetic field in the insulating material is
The magnetic energy stored in thecoaxial cable is
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Summary