The correct option is
A 24 NLet the wires lie in the x-y plane with the magnetic field in the -z direction as shown in the figure.
Force acting on a current carrying wire in a magnetic field is given by
→F=i(→l×→B)
=ilBsinθ ^n where
θ is the angle between the current element vector
→l and the magnetic field vector
→B and
^n represents the direction of force acting on the wire.
Here, current
i, length
l and magnetic field intensity
B are the same for all five wires. The angle
θ is also
90∘ for each of the wires since magnetic field is in the -z direction. Hence, the magnitude of magnetic force acting on each of the wires is going to be the same.
The direction of the force acting on the wires is different and is given by the direction of
→l×→B. The forces acting on each of the individual wires are shown in the diagram below.
Adding all the forces vectorially,
Fnet=2(2Fsin30∘)+F
=4F12+F=3F
=3ilBsin90∘
=3×2×1×4
=24 N