Practice portal › Moving Charges and Magnetism › Biot-Savart Law: Straight Wires and Arcs
A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle?
Asked in JEE Main 17th March 2nd Shift 2021 · Arcs and combined shapes
- (1) (μ₀ I)/(2π r)(2-π)
- (2) (μ₀ I)/(4π r)(2-π)
- (3) (μ₀ I)/(2π r)(2+π)
- (4) (μ₀ I)/(4π r)(2+π)
Answer: (4) (μ₀ I)/(4π r)(2+π)
Step-by-step solution
Semicircle: (μ₀ I)/(4r)
Each semi-infinite wire ends level with P: (μ₀ I)/(4π r) each, same sense as the arc.
B=(μ₀ I)/(4π r)(2+π)
Why the other options are wrong
- (1) Treats the straight parts as fully infinite wires and the semicircle as a full circle, with the arc opposing them
- (2) Makes the arc oppose the straight wires
- (3) Treats the straight parts as fully infinite wires and the semicircle as a full circle
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