An electron revolves around a nucleus with rotational frequency $f$ in a circular orbit. Due to this,the magnetic induction produced at the nucleus position is $B$. The radius of the circular orbit is directly proportional to:

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:

Write the formula for the magnetic field at a point on the axis of a circular current-carrying loop of radius $R$ at a distance $x$ from its center,where $x >> R$.

$A$ horizontal overhead powerline is at a height of $5 \,m$ from the ground and carries a current of $150 \,A$ from East to West. The magnetic field directly below it on the ground is

Current $I$ is flowing along the path $ABCDA$ consisting of four edges of a cube (figure $-a$),producing a magnetic field $B_0$ at the centre of the cube. Find the magnetic field $B$ produced at the center of the cube by a current $I$ flowing along the path of the six edges $ABCGHEA$ (figure $-b$).

$A$ coil having $9$ turns carrying current $I$ produces a magnetic field $B_1$ at the centre. If the same wire is rewound into a coil of $3$ turns carrying the same current $I$,then the magnetic field at the centre $B_2$ is: