The magnetic field at the centre $O$ in the given figure is

An electron $(e)$ moves in a circular orbit of radius '$r$' with uniform speed '$V$'. It produces a magnetic field '$B$' at the center of the circle. The magnetic field $B$ is ($\mu_0 =$ permeability of free space).

Consider a long straight wire of a circular cross-section (radius $a$) carrying a steady current $I$. The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field [inside the wire,outside the wire] is half of the maximum possible magnetic field,anywhere due to the wire,will be

$A$ long solenoid with $1000 \, \text{turns/m}$ has a core material with relative permeability $500$ and volume $10^{3} \, \text{cm}^{3}$. If the core material is replaced by another material having relative permeability of $750$ with the same volume, maintaining the same current of $0.75 \, \text{A}$ in the solenoid, the fractional change in the magnetic moment of the core would be approximately $\left(\frac{x}{499}\right)$. Find the value of $x$.

$A$ long straight wire of circular cross-section is made of a non-magnetic material. The wire is of radius $a$. The wire carries a current $I$ which is uniformly distributed over its cross-section. The energy stored per unit length in the magnetic field contained within the wire is

The magnetic field due to a current-carrying circular loop of radius $6 \ cm$ at a point on the axis at a distance of $8 \ cm$ from the centre is $216 \ \mu T$. Then the magnetic field at the centre of the ring is $\dots \ \mu T$.