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

Explanation

It forms a closed loop and the current completes the loop. Therefore, net force on the loop in uniform field should be zero. From the figure, net force on the loop in uniform field should be zero. In case (b) although it forms a closed loop, but current does not complete the loop. Hence, net force is not zero.

` therefore vecF_("loop") = vecF_(ACD) + vecF_(AD) = 2vecF_(AD) therefore |vecF_("loop") | = 2|vecF_(AD) |`
`2ilB sin theta (l =2r = 2.0 m ) = (2)(2)(2)(1) sin 90^@ = 8N`