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A circular arc of metallic wire subtends an angle π/2 at center. If it carries current I and its radius of curvature is r, then the magnetic field at the center of the arc is
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
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A circular arc of metallic wire subtends an angle π/2 at center. If...
The magnetic field at the centre of a circular arc carrying current can be determined using Biot-Savart's law. Here's the refined solution:
- The circular arc subtends an angle of π/2 at the centre.
- According to Biot-Savart's law, the magnetic field (B) due to a small current element is proportional to the current and inversely proportional to the square of the distance from the element.
- For a circular arc, the formula for the magnetic field at the centre is: B = (μ₀ × I × θ) / (4 × π × r).
- Here, μ₀ is the permeability of free space, I is the current, θ is the angle in radians, and r is the radius.
- Substitute θ = π/2 to get the magnetic field: B = (μ₀ × I) / (8 r).
A circular arc of metallic wire subtends an angle π/2 at the center. If it carries current I and its radius of curvature is r, then the magnetic field at the center of the arc is:
The magnetic field at the center of the arc can be calculated using the formula:
- The magnetic field B at the center is given by:
- B = (μ₀ I) / (4 π r)
- Where:
- μ₀ is the permeability of free space.
- I is the current flowing through the wire.
- r is the radius of the arc.
- For a circular arc subtending an angle of π/2, the effective contribution to the magnetic field is half that of a complete circular loop.
Thus, the magnetic field at the center of the arc is:
- B = (μ₀ I) / (8 π r)
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