Two identical circular wires of radius $20\,cm$ and carrying current $\sqrt{2}\,A$ are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wire is $.............\times 10^{-8}\,T$. (Take $\pi=3.14$ )

In hydrogen atom, an electron is revolving in the orbit of radius $0.53\,{\mathop A\limits^o }$ with $6.6 \times {10^{15}}$ $rotations/second$. Magnetic field produced at the centre of the orbit is.......$wb/{m^2}$

An $\alpha$ particle is moving along a circle of radius $R$ with a constant angular velocity $\omega $. Point $A$ lies in the same plane at a distance $2R$ from the centre. Point $A$ records magnetic field produced by $\alpha$ particle. If the minimum time interval between two successive times at which $A$ records zero magnetic field is $‘t’,$ find the angular speed $\omega $, in terms of $t.$

The ratio of the magnetic field at the centre of a current carrying coil of the radius $a$ and at a distance ‘$a$’ from centre of the coil and perpendicular to the axis of coil is

State scientists research about electricity and magnetism after Oersted’s observation.

Two concentric coils $X$ and $Y$ of radii $16 \,\,cm$ and $10 \,\,cm$ lie in the same vertical plane containing $N-S$ direction. $X$ has $20$ $turns$ and carries $16 \,\,A.$ $Y$ has $25$ $turns$ $\&$ carries $18\,A$. $X$ has current in anticlockwise direction and $Y$ has current in clockwise direction for an observer, looking at the coils facing the west. The magnitude of net magnetic field at their common centre is