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What would the Hall voltage be if a 2.00-T field is applied across a 10-gauge copper wire (2.588 mm in diameter) carrying a 20.0-A current?

a) 1.20 μV
b) 1.50 μV
c) 2.00 μV
d) 2.50 μV

Answer :

Final answer:

This question is about calculating the Hall voltage in a copper wire within a magnetic field. Without additional details from Example 20.6, we assume a 2.00-T field would induce a similar voltage as a calibrated probe, leading us to guess 1.20 μV as the closest answer (option a), although we cannot verify without further information from Example 20.6.

Explanation:

The student is asking about the calculation of the Hall voltage in a 10-gauge copper wire with a specific diameter, carrying a certain current, and placed within a magnetic field. The Hall voltage is a key concept in physics and is part of the study of electromagnetic phenomena. The formula for the Hall voltage (VH) is given as VH = BIl/nqA, where B is the magnetic field strength, I is the current, l is the length of the conductor across which the field is applied, n is the charge carrier density, q is the charge of the carrier, and A is the cross-sectional area of the conductor.

The variables n and q are properties of the conductor material and would typically be provided through examples or tables in physics textbooks. However, as these values are not provided in the question, we can follow a proportional approach because the question refers to 'using information in Example 20.6'. If we consider the Hall voltage is proportional to the magnetic field strength and inversely proportional to the diameter of the wire, as suggested by the additional information provided, we can estimate the Hall voltage when comparing to the calibrated Hall probe mentioned in passage 27, which suggests a direct proportionality between field strength and voltage.

If a probe is calibrated to give 1.00 µV under a 2.00-T field, we might then assume that the Hall voltage in our case, under the same 2.00-T field, would be the same if all other factors (like the charge carrier density and current dimensions) were equal. Therefore, the Hall voltage for the copper wire under the given conditions would be 1.00 µV. This assumption simplifies the calculation considerably, although it depends on the specific context provided by example 20.6 in the student's textbook, which is not available here.

Based on these assumptions and without additional specific information, the answer would correspond to option (a) 1.20 μV, assuming we round to the nearest option provided among the answers. However, without clear insight from Example 20.6, we cannot be certain this is the correct calculation. Hence, the mention of the correct option in the final part of the answer cannot be confirmed specifically but would logically be (a) 1.20 μV based on the information given.

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