ECE `106 - Magnetism and Magnetostatics

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Last updated 11:57 PM on 7/7/26
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9 Terms

1
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define Tesla =

magnetic field of a point charge

2
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Magnetic Force formula =

FB—> = qv→ × B→

3
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Lorentz force equation (E-field + M-field) =

F→ = qE→ + qv→B→

4
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Biot-Savart law / Magnetic field formula =

B→:

  • Point charge: (μo/4π)(qv→ × r^)/r² // image A

  • Current segment: (μo/4π)(Idl→ × r^)/r² // image B

  • Integral: (μo/4π)∫(Idl→ × r^)/r² // image C

where:

  • μo = permeability

  • I = current

  • q = charge

  • v→ = charge velocity

  • dl→ = current element

  • r = distance from dl→ to observation point where we want B→

<p>B<sup>→</sup>:</p><ul><li><p>Point charge: (μ<sub>o</sub>/4π)(qv<sup>→</sup> × r<sup>^</sup>)/r² // image A</p></li><li><p>Current segment: (μ<sub>o</sub>/4π)(Idl<sup>→</sup> × r<sup>^</sup>)/r² // image B</p></li><li><p>Integral: (μ<sub>o</sub>/4π)∫(Idl<sup>→</sup> × r<sup>^</sup>)/r² // image C</p></li></ul><p></p><p>where:</p><ul><li><p>μ<sub>o</sub> = permeability</p></li><li><p>I = current</p></li><li><p>q = charge</p></li><li><p>v<sup>→</sup> = charge velocity</p></li><li><p>dl<sup>→ </sup>= current element</p></li><li><p>r = distance from dl<sup>→</sup> to observation point where we want B<sup>→</sup></p></li></ul><p></p>
5
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Ampere’s Law =

∮c B→ · d𝓁→ = μ₀ I

  • holds for any C that COMPLETELY circles I

    • if it doesnt circle at all, = 0

  • loop MUST BE CLOSED

6
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Right hand rule for M-field =

Thumb:

  • points in direction of current

Fingers:

  • curl in direction of the magnetic field

7
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Cross product for cartesian coordinates =

x̂ → ŷ → ẑ → x̂

  • in this direction = POSITIVE

else NEGATIVE

8
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Cross product for cylindrical coordinates =

r̂ → φ̂ → ẑ → r̂

  • in this direction = POSITIVE

else NEGATIVE

9
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Cross product for spherical coordinates =

r̂ → θ̂ → φ̂ → r̂

  • in this direction = POSITIVE

else NEGATIVE