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 newton in both the cases `a` and `b`. The radius of the loop is 1.0 m
A
`4N`
B
`8N`
C
`10N`
D
`12N`
Text Solution
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The correct Answer is:
B
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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