A long solenoid has 70 turns / cm and carries current $I$. An electron moves within the solenoid in a circle of radius 2.5 cm perpendicular to the solenoid axis. If the speed of the electron is $4.4 \times 10^6 \mathrm{~m} / \mathrm{s}$, then the current $I$ in the solenoid is

(take $\mu_0=4 \pi \times 10^{-7}$ Si unit, mass electron $=9 \times 10^{-31}$

kg , charge of electron $1.6 \times 10^{-19} \mathrm{C}$ )

A current $I=5 \mathrm{~A}$ flows along a thin wire shaped as shown in figure. The radius of curved part of the wire is equal to $R=100 \mathrm{~mm}$, the angle $2 \phi=90^{\circ}$. The magnitude of magnetic field at the point $O$ is approximately

$$ \left(\text { use, } \frac{\mu_0}{4 \pi}=10^{-7} \mathrm{~T} \mathrm{~mA}^{-1}\right) $$

A toroid has a core (non-ferro magnetic) of inner radius 24 cm and outer radius 26 cm around which 2000 turns of a wire is wound. If the current in the wire is 12 A , the magnetic field inside the core of the toroid is

Two infinite wires carrying opposite electrical currents $I$ and $i$ are placed a distance $x$ apart. A point $P$ at a distance $y$ away from the wire carrying current $i$ is shown in the figure. If the magnetic field is zero at point $P$, then the magnitude of $i$ is