Practice portal › Moving Charges and Magnetism › Biot-Savart Law: Straight Wires and Arcs
Asked in NEET 2023 · Arcs and combined shapes
Given: two long straight sections along the same pair of horizontal lines, joined by a semicircle of radius R centred on P; A is directly above P and B directly below it.
Idea: add three contributions — the semicircle and the two semi-infinite straights, each with its own sign.
Semicircle: B=(μ₀i)/(4R). Running from A round the far side to B it circles P anticlockwise, so this points out of the page.
Each straight section ends on the perpendicular from P, so each gives B=(μ₀i)/(4π R).
The upper wire carries current towards A with P below it, and the lower carries current away from B with P above it; by the right-hand rule both point into the page.
Net: B=(μ₀i)/(4R)-2×(μ₀i)/(4π R)=(μ₀i)/(4R)[1-2/π].
Since 2/π≈0.64<1 the bracket is positive, so the result points out of the page.
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