The Earth's magnetic induction at a certain point is $7 \times 10^{-5} \ Wb/m^2$. This is to be annulled by the magnetic induction at the center of a circular conducting loop of radius $5 \ cm$. The required current in the loop is......$A$

$1 \ T = \dots \text{Gauss}$.

An element $\Delta l = \Delta x \hat{i}$ is placed at the origin and carries a current $I = 10 \,A$. The magnetic field on the $y$-axis at a distance of $0.5 \,m$ from the element of length $\Delta x = 1 \,cm$ is:

$A$ circular arc of radius $r$ carrying current $I$ subtends an angle $\frac{\pi}{16}$ at its centre. The radius of the metal wire is uniform. The magnetic induction at the centre of the circular arc is [where $\mu_0$ is the permeability of free space].

$PQRS$ is a square loop made of a uniform conducting wire. The current enters the loop at $P$ and leaves at $S$. Then the magnetic field will be

$A$ 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):