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

When equal current is passed through two coils, equal magnetic field is produced at their centres. If the ratio of number of turns in the coils is $8: 15$, then the ratio of their radii will be

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

Assertion : The magnetic field at the centre of the circular coil in the following figure due to the currents $I_1$ and $I_2$ is zero.

Reason : $I_1 = I_2$ implies that the fields due to the current $I_1$ and $I_2$ will be balanced.

Write Biot-Savart law.

Two concentric circular loops, one of radius $R$ and the other of radius $2 R$, lie in the $x y$-plane with the origin as their common center, as shown in the figure. The smaller loop carries current $I_1$ in the anti-clockwise direction and the larger loop carries current $I_2$ in the clockwise direction, with $I_2>2 I_1 . \vec{B}(x, y)$ denotes the magnetic field at a point $(x, y)$ in the $x y$-plane. Which of the following statement($s$) is(are) current?

$(A)$ $\vec{B}(x, y)$ is perpendicular to the $x y$-plane at any point in the plane

$(B)$ $|\vec{B}(x, y)|$ depends on $x$ and $y$ only through the radial distance $r=\sqrt{x^2+y^2}$

$(C)$ $|\vec{B}(x, y)|$ is non-zero at all points for $r$

$(D)$ $\vec{B}(x, y)$ points normally outward from the $x y$-plane for all the points between the two loops