A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field $\vec{B}$ = B₀ĵ as shown in the figure. The magnetic force on the wire if it has a current i is:
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Question

A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field $\vec{B}$ = B₀ĵ as shown in the figure. The magnetic force on the wire if it has a current i is:

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G1 Physics · Accepted Answer

Image For a wire segment in a uniform magnetic field: F⃗ = i l⃗ × B⃗ The effective length of the portion in the field is 2R. From the direction shown in the source figure, the force is along -ĵ. Therefore, F⃗ = -2iRB ĵ

A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immersed in a perpendicular magnetic field B ⃗ \vec{B} B = B₀ĵ as shown in the figure. The magnetic force on the wire if it has a current i is: