A circular loop carrying a current `I` is placed in the xy-plane as shown in figure. A uniform magnetic fied `B` is oriented along the positive z-axis. The loop tends to

Options

A. `A" "B" "C" "D`
`R,S" "R,S" "Q,R" "P,R`
B. `A" "B" "C" "D`
`Q,R" "R" "Q" "P,S`
C. `A" "B" "C" "D`
`P" "Q,R" "S" "Q,P`
D. `A" "B" "C" "D`
`Q" "R,S" "S" "P,Q`

Answer

A

Explanation

Because the magnetic field is parallel to X-axis, the force on wire parallel to X-axis is zero. The force on each wire parallel to Y-axis is `B_(0)i/2l`. Hence, net force on loop is `B_(0)Il`. Since, force on each wire parallel to Y-axis passes through centre of the loop net torque about centre of the loop is zero.
(B) Because the magnetic field is parallel to Y-axis, the force on wire parallel to Y-axis is zero. The force on each wire parallel to X-axis is `B_(0)i/2l`. Hence, net force on loop is `B_(0)il`. Since, force on each wire parallel to X-axis passes through centre of the loop, net torque about center of the loop is zero.
(C) Since, net displacement of current from entry point in the loop to exit point in the loop is along the diagonal of the loop. The direction of external uniform magnetic field is also along the same diagonal. Hence, net force on the loop is zero. Since, force on each wire on the loop passes through centre of the loop net torque about centre of the loop is zero.
(D) The net displacement of current from entry point in the loop to exit point in the loop is along the diagonal (of length `sqrt(2)l` of the loop. The direction of external uniform magnetic field is also perpendicular to the same diagonal. Hence, magnitude of net force on the loop is `B_(0)i(sqrt(2)l)`. Since, force on each wire on the loop passes through centre of the loop, net torque about centre of the loop is zero.
Hence, A-R, S, B-R, S, C-Q, R, D-P, R