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A current-carrying wire of infinite length is placed along the z-axis, carrying current I in the positive z-direction, generating a magnetic field B. What is the value of the line integral ∮ B⋅dℓ along a straight path connecting the points (−√3a, a, 0) and (a, a, 0)? [Here, μ₀ represents the permeability of free space.]
- 7μ₀I/24
- 7μ₀I/12
- μ₀I/8
- μ₀I/6
Correct answer: 7μ₀I/24
Solution
The value of the line integral ∮ B⋅dℓ along a straight path connecting the points (−√3a, a, 0) and (a, a, 0) is 7μ₀I/24 because the magnetic field B is perpendicular to the path, and the line integral can be evaluated using the Biot-Savart law, which gives the magnetic field at a point due to a current-carrying wire.
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