As shown in the figure, a uniform straight wire of length $30 \sqrt{3} \mathrm{~cm}$ is bent in the form of an equilateral triangle $A B C$. A uniform magnetic field $2 T$ is applied parallel to the side $B C$. If the current through the wire is 2 A , the magnitude of the force on the side $A C$ is ( $\bar{B}$ represents the direction of the magnetic field)

A proton moving with a velocity of $8 \times 10^5 \mathrm{~ms}^{-1}$ enters a uniform magnetic fleld normal to the direction of the magnetic field. If the radius of the circular path of the proton in the magnetic field is 8.3 cm , then the magnitude of the magnetic field is

(Charge of proton $=1.6 \times 10^{-19} \mathrm{C}$ and mass of the proton $=1.66 \times 10^{-27} \mathrm{~kg}$ )

The number of turns of two circular coils $A$ and $B$ are 300 and 200 respectively. The magnetic moments of the two coils $A$ and $B$ are in the ratio $1: 2$. If the two coils carry equal currents, then the ratio of radii of coils $A$ and $B$ is

Two long straight parallel wires carry currents of 8 A and 10 A in opposite directions. If the distance of separation between the wires is 9 cm , then the net magnetic field at a point between the two wires, which is at a perpendicular distance of 4 cm from the wire carrying 8 A current is