The is a fascinating phenomenon in conducting materials exposed to magnetic fields. It reveals crucial information about , helping us understand the behavior of and in various materials.
Velocity selectors and calculations demonstrate practical applications of the . These concepts are essential for understanding charge carrier dynamics and material properties, connecting electromagnetic theory to real-world applications in electronics and materials science.
The Hall Effect
Hall effect in conducting materials
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11.6 The Hall Effect – University Physics Volume 2 View original
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Phenomenon observed in conductors and placed in a magnetic field perpendicular to electric current flow
Generates a () perpendicular to both current and magnetic field
voltage is the potential difference across the conductor, perpendicular to current flow
Caused by the acting on charge carriers
Deflects charge carriers (electrons or holes) to one side of the conductor, creating a charge imbalance
Charge imbalance results in the Hall voltage
Significant in determining charge carrier properties in conducting materials
Sign of Hall voltage indicates type of charge carriers (electrons or holes)
Magnitude of Hall voltage is proportional to and
(RH) relates Hall voltage to current, magnetic field, and conductor thickness
RH=JxBzEH=ne1, where EH is Hall field, Jx is current density, Bz is magnetic field, n is charge carrier density, and e is elementary charge
Sign and magnitude of Hall coefficient provide information about charge carrier type and density (semiconductors, metals)
Force balance in velocity selectors
uses combination of electric and magnetic fields to select particles with specific velocity
Electric field (E) and magnetic field (B) applied perpendicular to each other and particle motion direction
For particle with charge q and velocity v, electric force (FE) and magnetic force (FB) act on particle
Electric force given by FE=qE
Magnetic force given by FB=qv×B
When electric and magnetic forces balance, particle passes through undeflected
Occurs when ∣FE∣=∣FB∣, or ∣qE∣=∣qv×B∣
Simplifies to ∣E∣=∣v×B∣ or E=vBsinθ, where θ is angle between v and B
Adjusting electric and magnetic field strengths selects particles with specific velocity (mass spectrometry, particle accelerators)
Calculation of Hall voltage
Hall voltage (VH) is potential difference across conductor in presence of magnetic field and electric current
Calculation requires current (I), magnetic field strength (B), and charge carrier properties (density n and elementary charge e) of conductor
Hall voltage given by VH=ntqIB, where t is conductor thickness and q is charge of carriers (positive for holes, negative for electrons)
Alternatively, use Hall coefficient (RH) to calculate Hall voltage: VH=tIRHB
Hall coefficient related to charge carrier density and elementary charge by RH=nq1
To calculate Hall voltage:
Identify given values for current (I), magnetic field strength (B), conductor thickness (t), and either Hall coefficient (RH) or charge carrier density (n) and elementary charge (q)
If Hall coefficient not given, calculate using RH=nq1
Substitute values into appropriate equation: VH=ntqIB or VH=tIRHB
Solve for Hall voltage (VH), ensuring consistent units throughout calculation
Charge carrier dynamics and material properties
: average velocity of charge carriers in response to an applied electric field
Mobility: measure of how easily charge carriers move through a material in response to an electric field
Related to and electric field strength
: measure of a material's ability to conduct electric current
Depends on charge carrier density, mobility, and charge