Tesla is a unit for measuring

$A$ current $I$ flows in a wire bent in the shape of a quarter ring of radius $R$ as shown in the figure. The magnetic field induction $B$ at point $O$ is

Find the magnetic field at $O$.

The magnetic field at the origin due to the current $I$ flowing in the wire as shown in the figure is:

Write the formula for the magnetic field at a perpendicular distance $r$ from a finite current-carrying wire.

$A$ 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 $x$.