Physics Moving Charges and Magnetism

A wire $A$ $$ , bent in the shape of an arc of a circle, carrying a current of $$ $2\mathrm{A}$ and having radius $2\mathrm{c}\mathrm{m}$ $$ and another wire $B$ $$ , also bent in the shape of arc of a circle, carrying a current of $3\mathrm{A}$ $$ and having radius of $4\mathrm{c}\mathrm{m}$ $$ , are placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ $$ and B$$ at the common centre 0 is:

If momentum (P), area (A) and time (T) are taken to be the fundamental quantities, then the dimensional formula for energy is :

The figure shows a region of length 'l' with a uniform magnetic field of 0.3 T in it and a proton entering the region with velocity 4 × 10⁵ ms⁻¹ making an angle 60° with the field. If the proton completes 10 revolution by the time it cross the region shown, 'l' is close to (mass of proton = 1.67 × 10⁻²⁷ kg, charge of the proton = 1.6 × 10⁻¹⁹C)

A beam of protons with speed 4 × 10⁵ ms⁻¹ enters a uniform magnetic field of 0.3 T at an angle of 60° to the magnetic field. The pitch of the resulting helical path of protons is close to: (Mass of the proton = 1.67 × 10⁻²⁷ kg, charge of the proton = 1.69 × 10⁻¹⁹ C)

An electron is moving along +x direction with a velocity of 6 × 10? ms?¹. It enters a region of uniform electric field of 300 V/cm pointing along +y direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the x direction will be:
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A particle of charge q and mass m is moving with a velocity -vi (v ≠ 0) towards a large screen placed in the Y-Z plane at a distance d. If there is a magnetic field B = B?k, the minimum value of v for which the particle will not hit the screen is:
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