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Two metallic strips (1 and 2) have identical dimensions (length l, width w, thickness d) but different charge-carrier densities n1 and n2. Strip 1 sits in a magnetic field B1 and strip 2 in a magnetic field B2, both fields pointing along +y. The same current I flows through each strip, producing Hall potential differences V1 and V2 between the edges K and M. Which statement(s) is/are correct?
- If B1 = B2 and n1 = 2n2, then V2 = 2V1
- If B1 = B2 and n1 = 2n2, then V2 = V1
- If B1 = 2B2 and n1 = n2, then V2 = 0.5V1
- If B1 = 2B2 and n1 = n2, then V2 = V1
Correct answer: If B1 = B2 and n1 = 2n2, then V2 = 2V1
Solution
Hall voltage V = IB/(ned). With identical thickness and current, V depends only on B/n. For B1=B2 and n1=2n2: V2/V1 = (n1/n2) = 2, so V2 = 2V1. For B1=2B2 and n1=n2: V2/V1 = B2/B1 = 1/2, so V2 = 0.5V1 (which means V1 = 2V2, not the options 0.5V1 or equal as paired with the stated condition). The clean correct pairing is V2 = 2V1 under the first condition.
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