When a certain length of wire is turned into one circular loop,the magnetic induction at the centre of the coil due to a current $I$ flowing through it is $B_1$. If the same wire is turned into three loops to make a circular coil,the magnetic induction at the center of this coil for the same current will be:

Consider a tightly wound $100$ turn coil of radius $10 \,cm$ carrying a current of $2 \,A$. The magnitude of the magnetic field at the centre of the coil is

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):

The magnetic field at a point $P$ situated at a perpendicular distance $R$ from a long straight wire carrying a current of $12 \ A$ is $3 \times 10^{-5} \ Wb/m^2$. The value of $R$ in $mm$ is $\left[\mu_0 = 4\pi \times 10^{-7} \ Wb/Am\right]$

$A$ 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 $x$.

$A$ wire $A$, bent in the shape of an arc of a circle, carrying a current of $2 \, A$ and having radius $2 \, cm$, and another wire $B$, also bent in the shape of an arc of a circle, carrying a current of $3 \, A$ and having radius $4 \, cm$, are placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ and $B$ at the common centre $O$ is