For the circuit shown in the figure, the current through $6 \Omega$ resistor connected between the junctions $A$ and $B$ is

The area of cross-section of a potentiometer wire is $6 \times 10^{-7} \mathrm{~m}^2$. The potential difference per unit length of the potentiometer wire when it is connected to a cell of negligible internal resistance and a resistor in series is $0.15 \mathrm{Vm}^{-1}$. If the current through potentiometer wire is 0.3 A , then the resistivity of the material of the potentiometer wire is

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 $=1.66 \times 10^{-27} \mathrm{~kg}$ )