In the figure shown a semicircular wire loop is placed in a uniform magnetic field $B = 1.0 T$ . The plane of the loop is perpendicular to the magnetic field. Current $i = 2 A$ flows in the loop in the directions shown. Find the magnitude of the magnetic force in case $(a)$ . The radius of the loop is $1.0 m$ .
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$F_{m} = 2 N$

$F_{m} = 0$

$F_{m} = 4 N$

$F_{m} = 1 N$

answer is A.

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Detailed Solution

Referring to figure $(a)$ ,

It forms a closed loop and the current completes the loop. Therefore, net force on the loop in uniform field should be zero.

$F_{A C D} = F_{A D} ∴ F_{l o o p} = F_{A C D} + F_{A D} = 2 F_{A D} ∴ |F_{l o o p}| = 2 |F_{A D}| = 2 i l B \sin θ = (2) (2) (2) (1) \sin 90 ° = 8 N$

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