$A$ current of $0.1\, A$ circulates around a coil of $100$ turns and having a radius equal to $5\, cm$. The magnetic field set up at the centre of the coil is $(\mu_0 = 4\pi \times 10^{-7} \, Wb/A \cdot m)$

$A$ Helmholtz coil has a pair of loops,each with $N$ turns and radius $R$. They are placed coaxially at a distance $R$ apart,and the same current $I$ flows through the loops in the same direction. The magnitude of the magnetic field at $P$,the midpoint between the centers $A$ and $C$,is given by (Refer to figure):

$A$ coil of one turn is made of a wire of a certain length,and then from the same length of wire,a coil of two turns is made. If the same current is passed in both cases,what is the ratio of the magnetic inductions at their centers?

Let $B_1$ be the magnitude of the magnetic field at the center of a circular coil of radius $R$ carrying current $I$. Let $B_2$ be the magnitude of the magnetic field at an axial distance $x$ from the center. For $x : R = 3 : 4$,the ratio $\frac{B_2}{B_1}$ is:

Two long straight parallel conductors $A$ and $B$ carrying currents $4.5 \ A$ and $8 \ A$ respectively are separated by $25 \ cm$ in air. The resultant magnetic field at a point $P$ which is at a distance of $15 \ cm$ from conductor $A$ and $10 \ cm$ from conductor $B$ is:

Two mutually perpendicular insulated conducting wires carrying equal currents $I$ intersect at the origin. The resultant magnetic induction at point $P(2 \ m, 3 \ m)$ will be: