16 lines
1.1 KiB
Markdown
16 lines
1.1 KiB
Markdown
- Magnetic fields are represented with the symbol $\vec{B}$
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- Magnetism is based in *electric charge*, specifically the motion of that charge.
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- The magnetic force is always at right angles to both the velocity $\vec{v}$, and the magnetic field $\vec{B}$
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- The force is greatest when the charge is moving at right angles and is zero for motion parallel to the field. THe force is generally proportional to $\sin(\theta)$, where $\theta$ is the angle between the velocity $\vec{v}$, and the field $\vec{B}$.
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The formula that describes magnetic force compactly is:
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$$ \vec(F_B) = q\vec(v) \times \vec{B} $$
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- $F_B$ is the magnetic force
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- $q$ is the charge the force is acting on
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- $v$ is the velocity of the charge
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- $B$ is the magnetic field
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For the magnitude of a magnetic force:
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$$ |\vec(F_B)| = |q|vB\sin(\theta) $$
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For the radius of a particle's circular path:
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$$ r = \frac{mv}{qB} $$For the period of a particle's circular orbit in a uniform magnetic field:
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$$ T = \frac{2\pi r}{v} = \frac{2\pi}{v}\frac{mv}{qB} = \frac{2\pi m}{qB} $$
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- The period is independent of the particle's speed and orbital radius. |