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In the figure shown a semicircular wire ...

In the figure shown a semicircular wire loop is placed in a uniform magnetic field `B=1.0T`. The plane of the loop is perpendicular to the magnetic field. Current `i=2A` flows in the loop in the directions shown. Find the magnitude of the magnetic force in both the cases `a` and `b`. The radius of the loop is 1.0 m

Text Solution

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Refer Fig. It forms a closed loop and the current completes the loop. Therefore, net force on the loop in uniform field should be zero.
Refer Fig. In this case although it forms a closed loop, but current does not complete the loop. Hence, net force is not zero.
`vecF_(ACD)=vecF_(AD)`
`:. vecF_("loop")=vecF_(ACD)+vecF_(AD)=2vecF_(AD)`
`:. |vecF_("loop")|=2|vecF_(AD)|`
`=2ilB sin theta (l=2r=2.0m)`
`=(2)(2)(2)(1) sin 90^@=8N`
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