Respuesta :
Answer:
[tex]n =1.31172 \times 10^{26}\ electron/m^3[/tex]
Explanation:
given,
magnetic field strength = 0.875 T
thickness of strip = 0.102 mm
Current = 3.89 A
Hall voltage = 1.59 mV
electron density calculation:-
we know,
[tex]V = \dfrac{iB}{neL}[/tex]
[tex]n = \dfrac{iB}{eVL}[/tex]
[tex]n = \dfrac{3.89 \times 0.875}{1.6 \times 10^{-19}\times 1.59 \times 10^{-3}\times 1.59 \times 10^{-3}}[/tex]
[tex]n = \dfrac{3.40375}{0.259488 \times 10^{-25}}[/tex]
[tex]n =13.1172 \times 10^{25}[/tex]
[tex]n =1.31172 \times 10^{26}\ electron/m^3[/tex]
The density of mobile electrons in the material whose thin strip is used to investigated is immersed in a magnetic field is 1.312×10²⁶ m⁻³.
What is magnetic field?
The magnetic field is the field in the space and around the magnet in which the magnetic field can be fill.
The magnetic field experienced by a charged particle can be given as,
[tex]B=qL\dfrac{V}{I}[/tex]
Here, (q) is the charge of the particle, (V) is the voltage,(L) is the length and (I) is the current.
As the charge is the product of number of electron times charge on one electron. Therefore, the above formula can be written as,
[tex]B=n(1.6\times10^{-19})L\dfrac{V}{I}[/tex]
Here, (n) is the number of electron.
The magnetic field strength was 0.875 T, the strip was 0.102 mm thick, the current along the strip was 3.89 A, and the Hall voltage between the strip's edges was 1.59 mV.
Thus put these values in the above expression as,
[tex]0.875=n(1.6\times10^{-19})(0.102\times10^{-3})\dfrac{1.59\times10^{-3}}{3.89}\\n=1.312\times10^{26}\rm[/tex]
thus, the density of mobile electrons in the material whose thin strip is used to investigated is immersed in a magnetic field is 1.312×10²⁶ m⁻³.
Learn more about magnetic field here;
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