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phy142:lectures:17 [2014/03/14 10:04] mdawber [Video of lecture] |
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+ | ===== Hall Effect ===== | ||

+ | |||

+ | If we have a magnetic field applied at right angles to a current carrying wire the charges moving in the conductor will experience a magnetic force. The charge carriers in the conductor will redistribute themselves to produce an internal electric field at right angles to the current and field so that the net force on a charge carrier is zero (or in other words, the system is in equilibrium). The size of the field can be found by considering the Lorentz equation. | ||

+ | |||

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+ | $\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})$ | ||

+ | |||

+ | The field required to achieve equilibrium is | ||

+ | |||

+ | $E_{H}=v_{d}B$ | ||

+ | |||

+ | where we should recall that $v_{d}$ is the drift velocity of the carriers in the conductor. | ||

+ | |||

+ | What is neat about the [[wp>Hall_effect|Hall effect]] is that the direction of the field depends on whether the carriers are positive or negative charges. The Hall field $E_{H}$ leads to a Hall emf across the sample proportional to it's thickness $\mathcal{E}_{H}=E_{ | ||

+ | H}d=v_{d}Bd$ | ||

+ | |||

+ | {{halleffect.png}} | ||

+ | |||

+ | ===== Mass Spectrometer ===== | ||

+ | |||

+ | A [[wp>Mass_spectrometry|mass spectrometer]] separates particles according their mass to charge ratio. | ||

+ | |||

+ | Combining the Lorentz equation $\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})$ with Newton's Second Law | ||

+ | $\vec{F}=m\vec{a}$ gives us the equation of motion for charged particles in electromagnetic fields | ||

+ | |||

+ | $\frac{m}{q}\vec{a}=(\vec{E}+\vec{v}\times\vec{B})$ | ||

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+ | Various methods can be used to separate the particles according to their $\frac{m}{q}$ ratio. | ||

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===== Galvanometer ===== | ===== Galvanometer ===== | ||

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{{homopolarmotor.png}} | {{homopolarmotor.png}} | ||

- | ===== Hall Effect ===== | ||

- | |||

- | In the example we just discussed we saw that if we have a magnetic field applied at right angles to a current carrying wire the charges moving in the conductor will experience a magnetic force. The charge carriers in the conductor will redistribute themselves to produce an internal electric field at right angles to the current and field so that the net force on a charge carrier is zero (or in other words, the system is in equilibrium). The size of the field can be found by considering the Lorentz equation. | ||

- | |||

- | |||

- | $\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})$ | ||

- | |||

- | The field required to achieve equilibrium is | ||

- | |||

- | $E_{H}=v_{d}B$ | ||

- | |||

- | where we should recall that $v_{d}$ is the drift velocity of the carriers in the conductor. | ||

- | |||

- | What is neat about the [[wp>Hall_effect|Hall effect]] is that the direction of the field depends on whether the carriers are positive or negative charges. The Hall field $E_{H}$ leads to a Hall emf across the sample proportional to it's thickness $\mathcal{E}_{H}=E_{ | ||

- | H}d=v_{d}Bd$ | ||

- | |||

- | {{halleffect.png}} | ||

- | ===== Mass Spectrometer ===== | ||

- | |||

- | A [[wp>Mass_spectrometry|mass spectrometer]] separates particles according their mass to charge ratio. | ||

- | |||

- | Combining the Lorentz equation $\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})$ with Newton's Second Law | ||

- | $\vec{F}=m\vec{a}$ gives us the equation of motion for charged particles in electromagnetic fields | ||

- | |||

- | $\frac{m}{q}\vec{a}=(\vec{E}+\vec{v}\times\vec{B})$ | ||

- | |||

- | Various methods can be used to separate the particles according to their $\frac{m}{q}$ ratio. | ||