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A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y-Z plane. Magnetic field at point O is:

1. B = - μ₀ / 4π × I / R (μî × k̂)
2. B = - μ₀ / 4π × I / R (πî + k̂)
3. Option (c)
4. Option (d)

Correct answer: B = - μ₀ / 4π × I / R (μî × k̂)

Solution

The magnetic field at the center of a semicircular current-carrying wire is given by B = (μ₀I)/(4R). The direction of the field is determined using the right-hand rule, which gives the cross product μî × k̂. Thus, the correct answer is option A.

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