A proton moving with a velocity of 8 × 105 ms-1 enters a uniform magnetic field perpendicular 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 × 10-19 C and mass of proton = 1.66 × 10-27 kg)

A uniform straight wire of length 30√3 cm is bent in the form of an equilateral triangle ABC. A uniform magnetic field of 2 T is applied parallel to the side BC. If the current through the wire is 2 A, the magnitude of the force on the side AC is:

At a certain place in the magnetic meridian, the total earth's magnetic field is twice its vertical component. The ratio of the horizontal component of the earth's magnetic field to the total magnetic field of the earth at that place is: