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For an infinite linear current, four loops are shown in the given figure. The magnetic flux should be the maximum through the loop number—
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- 1
- 2
- 3
- 4
Correct Option: B
All the loops have equal areas. B at any distance r from the wire is k/ r. For any rectangular loop of height h (in the direction of the wire) and width w (⊥ the wire), the flux φ is
![]() | a + w | ∞ | = kh ln | a | r | a |
where a is the distance of the near side from the wire.
Thus,
for 1, φ1 = k l ln | a |
for 2, φ2 = k 2l ln | a |
for 3, φ3 = | k2l ln | 2 | a + 1/4 |
for 4, φ4 = | kl ln | |
a |
φ1 = kl ln | ![]() | 1 + | ![]() | ,φ2 = 2kl ln | ![]() | 1 + | ![]() | ||
a | a |
φ3 = kl ln | ![]() | 1 + | ![]() | ,φ4 = | kl ln | ![]() | 1 + | ![]() | ||||
a + 1/4 | 2 | a |
The long terms do not change by significant amount. Thus, φ2 should be of highest value.
Hence alternative (B) is the correct choice.