In the hydrogen atom, the electron is making $6.6 \times {10^{15}}\,r.p.s.$ If the radius of the orbit is $0.53 \times {10^{ - 10}}\,metre,$ then magnetic field produced at the centre of the orbit is......$Tesla$

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

Give differences between Biot-Savart law and Coulomb’s law.

A circular loop is kept in that vertical plane which contains the north-south direction. It carries a current that is towards south at the topmost point. Let $A$ be a point on axis of the circle to the east of it and $B$ a point on this axis to the west of it. The magnetic field due to the loop :-

A long conducting wire having a current $I$ flowing through it, is bent into a circular coil of $N$ turns.Then it is bent into a circular coil of $n$ tums. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is:

A coil having $N$ $turns$ is wound tightly in the form of a spiral with inner and outer radii $a$ and $b$ respectively. When a current $I$ passes through the coil, the magnetic field at the centre is