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For an n-type Ge specimen, width = 4 mm, length = 1 mm, current (along the length of specimen) = 1 mA, magnetic field (perpendicular to the current flow direction) = 0.1 Wb/m2 and Hall voltage magnitude = 0.005 V. Calculate the majority carriers density.
- a)3 × 1019 cm-3
- b)3 × 1019 m-3
- c)6 × 1019 cm-3
- d)6 × 1019 m-3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
For an n-type Ge specimen, width = 4 mm, length = 1 mm, current (along...
To calculate the majority carrier density, we can use the formula for Hall coefficient:
R_H = V_H / (I * B * d)
where R_H is the Hall coefficient, V_H is the Hall voltage magnitude, I is the current, B is the magnetic field, and d is the thickness of the specimen.
Rearranging the formula, we get:
n = 1 / (R_H * q)
where n is the majority carrier density and q is the charge of an electron.
Given:
V_H = 0.005 V
I = 1 mA = 0.001 A
B = 0.1 Wb/m^2
d = 4 mm = 0.004 m
The Hall coefficient can be calculated as:
R_H = V_H / (I * B * d)
= 0.005 V / (0.001 A * 0.1 Wb/m^2 * 0.004 m)
= 125 V/A/m^2
The charge of an electron is q = 1.6 x 10^-19 C.
Substituting the values into the formula for majority carrier density:
n = 1 / (R_H * q)
= 1 / (125 V/A/m^2 * 1.6 x 10^-19 C)
= 1 / (2 x 10^-17 V/A/m^2)
= 5 x 10^16 m^-3
Therefore, the majority carrier density is 5 x 10^16 m^-3.
R_H = V_H / (I * B * d)
where R_H is the Hall coefficient, V_H is the Hall voltage magnitude, I is the current, B is the magnetic field, and d is the thickness of the specimen.
Rearranging the formula, we get:
n = 1 / (R_H * q)
where n is the majority carrier density and q is the charge of an electron.
Given:
V_H = 0.005 V
I = 1 mA = 0.001 A
B = 0.1 Wb/m^2
d = 4 mm = 0.004 m
The Hall coefficient can be calculated as:
R_H = V_H / (I * B * d)
= 0.005 V / (0.001 A * 0.1 Wb/m^2 * 0.004 m)
= 125 V/A/m^2
The charge of an electron is q = 1.6 x 10^-19 C.
Substituting the values into the formula for majority carrier density:
n = 1 / (R_H * q)
= 1 / (125 V/A/m^2 * 1.6 x 10^-19 C)
= 1 / (2 x 10^-17 V/A/m^2)
= 5 x 10^16 m^-3
Therefore, the majority carrier density is 5 x 10^16 m^-3.
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Community Answer
For an n-type Ge specimen, width = 4 mm, length = 1 mm, current (along...
Concept:
The hall voltage VA is given by:
ρc: Charge density
RH: Hall coefficient
W is the side across which the magnetic field is applied.
Calculation:
W = Thickness = 4 mm, I = 1 mA, VH = 0.005 V, B = 0.1 Wb/m2
Since hall voltage is positive, the majority charge carriers will be holes, with the concentration calculated as:
p ≈ 3 × 1019 m-3
The hall voltage VA is given by:
ρc: Charge density
RH: Hall coefficient
W is the side across which the magnetic field is applied.
Calculation:
W = Thickness = 4 mm, I = 1 mA, VH = 0.005 V, B = 0.1 Wb/m2
Since hall voltage is positive, the majority charge carriers will be holes, with the concentration calculated as:
p ≈ 3 × 1019 m-3
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For an n-type Ge specimen, width = 4 mm, length = 1 mm, current (along the length of specimen) = 1 mA, magnetic field (perpendicular to the current flow direction) = 0.1 Wb/m2 and Hall voltage magnitude = 0.005 V. Calculate the majority carriers density.a)3 × 1019 cm-3b)3 × 1019 m-3c)6 × 1019 cm-3d)6 × 1019 m-3Correct answer is option 'B'. Can you explain this answer?
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