Home » Electromagnetic Theory » Electromagnetic theory miscellaneous » Question

Electromagnetic theory miscellaneous

Electromagnetic Theory

  1. For an infinite linear current, four loops are shown in the given figure. The magnetic flux should be the maximum through the loop number—
    1. 1
    2. 2
    3. 3
    4. 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
khdr
= kh ln
a + w
ara

where a is the distance of the near side from the wire.
Thus,
for 1, φ1 = k l ln
a + 1
a

for 2, φ2 = k 2l ln
a + 1/2
a

for 3, φ3 =
1
k2l ln
a + 1/4 + 1
2a + 1/4

for 4, φ4 = kl ln
a + 2 l
a

φ1 = kl ln 1 +
1
2 = 2kl ln 1 +
1
aa

φ3 = kl ln 1 +
1
4 =
1
kl ln 1 +
2 l
a + 1/42a

The long terms do not change by significant amount. Thus, φ2 should be of highest value.
Hence alternative (B) is the correct choice.



Your comments will be displayed only after manual approval.