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Two metallic strips (labelled 1 and 2) made of the same material have equal lengths. Strip 1 has width w1 and thickness d1, while strip 2 has width w2 and thickness d2. Points K and M lie symmetrically on the two opposite faces that are parallel to the x-y plane. When a steady current I passes through each strip placed in a uniform magnetic field B, V1 and V2 denote the Hall potential differences developed between K and M in strips 1 and 2 respectively. Which of the following statement(s) is/are correct?

1. If w1 = w2 and d1 = 2d2, then V2 = 2V1
2. If w1 = w2 and d1 = 2d2, then V2 = V1
3. If w1 = 2w2 and d1 = d2, then V2 = 2V1
4. If w1 = 2w2 and d1 = d2, then V2 = V1

Correct answer: If w1 = w2 and d1 = 2d2, then V2 = 2V1

Solution

The Hall voltage is V_H = B*I/(n*e*d), where d is the strip thickness along the field. It is independent of the width w. So V is inversely proportional to thickness d only.

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