An electron having kinetic energy of 100 eV circulates in a path of radius 10 cm in a magnetic field. The magnitude of magnetic field $$|\mathbf{B}|$$ is approximately [Mass of electron $$=0.5 \mathrm{~MeV} \mathrm{c}^{-2}$$, where c is the velocity of light].

A particle of mass $$2.2 \times 10^{-30} \mathrm{~kg}$$ and charge $$1.6 \times 10^{-19} \mathrm{C}$$ is moving at a speed of $$10 \mathrm{~km} \mathrm{~s}^{-1}$$ in a circular path of radius 2.8 cm inside a solenoid. The solenoid has $$25 \frac{\text { turns }}{\mathrm{cm}}$$ and its magnetic field is perpendicular to the plane of the particle's path. The current in the solenoid is

(Take, $$\mu_0=4 \pi \times 10^{-7} \mathrm{~Hm}^{-1}$$)

A toroid has a non ferromagnetic core of inner radius 24 cm and outer radius 25 cm , around which 4900 turns of a wire are wound. If the current in the wire is 12 A , the magnetic field inside the core of the toroid is