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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 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.

Refer figure b. In this case although it forms a closed loop, but current does not complete the loop. Hence, net force is not zero.
`F_(ACD)=F_(AD)`
`:.F_(loop)=F_(ACD)+F_(AD)=2F_(AD)`
`:. |F_(loop)|=2|F_(AD)|`
`2ilB sintheta [l=2r=2.0m]`
`=(2)(2)(2)(1)sin90^@=8N`
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