Q. 5: (a)The Hall effect can be used to calculate the charge-carrier number density in a di0 2i 1ed conductor. If a conductor carrying a current of 2.0 A is 0.5 mm thick, and the Hall effect bognvoltage is 4.5µV when it is in a uniform magnetic field of 1.2 T, what is the density of lotar charge carriers in the conductor? bo sdiaAboen on

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**Question 5: (a)** The Hall effect can be used to calculate the charge-carrier number density in a conductor. If a conductor carrying a current of 2.0 A is 0.5 mm thick, and the Hall effect voltage is 4.5 μV when it is in a uniform magnetic field of 1.2 T, what is the density of charge carriers in the conductor?

*Explanation:*

The Hall effect is a phenomenon in which a voltage difference (Hall voltage) is produced across an electrical conductor when it is placed in a magnetic field perpendicular to the current. This effect can be used to determine the density of charge carriers (such as electrons) in the conductor.

To calculate the charge-carrier number density (\( n \)), the Hall effect equation can be utilized:

\[ V_H = \frac{IB}{nq} \]

Where:
- \( V_H \) is the Hall voltage (4.5 μV),
- \( I \) is the current (2.0 A),
- \( B \) is the magnetic field (1.2 T),
- \( q \) is the charge of an electron (\( 1.6 \times 10^{-19} \) C).

The thickness of the conductor is used in calculations to determine the area through which current flows. The number density \( n \) can be rearranged and calculated as follows:

\[ n = \frac{IB}{V_H q} \]

**Graph/Diagram Explanation:**

There is a faint diagram that resembles a simple circuit with a resistor and other components. However, due to its poor visibility, specific details about the diagram cannot be accurately described.
Transcribed Image Text:**Question 5: (a)** The Hall effect can be used to calculate the charge-carrier number density in a conductor. If a conductor carrying a current of 2.0 A is 0.5 mm thick, and the Hall effect voltage is 4.5 μV when it is in a uniform magnetic field of 1.2 T, what is the density of charge carriers in the conductor? *Explanation:* The Hall effect is a phenomenon in which a voltage difference (Hall voltage) is produced across an electrical conductor when it is placed in a magnetic field perpendicular to the current. This effect can be used to determine the density of charge carriers (such as electrons) in the conductor. To calculate the charge-carrier number density (\( n \)), the Hall effect equation can be utilized: \[ V_H = \frac{IB}{nq} \] Where: - \( V_H \) is the Hall voltage (4.5 μV), - \( I \) is the current (2.0 A), - \( B \) is the magnetic field (1.2 T), - \( q \) is the charge of an electron (\( 1.6 \times 10^{-19} \) C). The thickness of the conductor is used in calculations to determine the area through which current flows. The number density \( n \) can be rearranged and calculated as follows: \[ n = \frac{IB}{V_H q} \] **Graph/Diagram Explanation:** There is a faint diagram that resembles a simple circuit with a resistor and other components. However, due to its poor visibility, specific details about the diagram cannot be accurately described.
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