$A$ helium nucleus makes a full rotation in a circle of radius $0.8 \ m$ in $2 \ s$. The value of the magnetic field $B$ at the centre of the circle will be

The magnetic induction at point $O$ for the current-carrying wire shown in the figure is:

If the current flowing through the shell of the previous objective is equal to $i$,then the energy density at a point at a distance $2R$ from the axis of the shell varies according to which graph?

An electron moves in a circular orbit with uniform speed $v$. It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is (where $\mu_{0} =$ permeability of free space,$e =$ electronic charge):

$A$ long solenoid has $100 \, \text{turns/m}$ and carries current $i$. An electron moves within the solenoid in a circle of radius $2.30 \, \text{cm}$ perpendicular to the solenoid axis. The speed of the electron is $0.046 \, c$ ($c = 3 \times 10^8 \, \text{m/s}$ is the speed of light). Find the current $i$ in the solenoid (approximate). (in $ \text{A}$)

$A$ vertical straight conductor carries a current vertically upwards. $A$ point $P$ lies to the east of it at a small distance and another point $Q$ lies to the west at the same distance. The magnetic field at $P$ is