$A$ conducting circular loop of copper is placed as shown in the figure. The cross-sectional area of part $abc$ is $A$ and that of part $adc$ is $A/3$. The magnetic field at point $O$ is:

Two concentric coils of $20$ turns each are placed in the same plane. Their radii are $30 \text{ cm}$ and $60 \text{ cm}$,and they carry $0.4 \text{ A}$ and $0.6 \text{ A}$ currents,respectively,in opposite directions. The magnetic induction at the centre in tesla is ....... .

$A$ point charge $Q (= 3 \times 10^{-12} \, C)$ rotates uniformly in a vertical circle of radius $R (= 1 \, mm)$. The axis of the circle is aligned along the magnetic axis of the earth. At what value of the angular speed $\omega$,the effective magnetic field at the centre of the circle will be reduced to zero? (Horizontal component of earth's magnetic field is $30 \, \mu T$)

$A$ long straight wire carrying current $16 \,A$ is bent at $90^{\circ}$ such that one segment lies along the positive $x$-axis and the other segment lies along the positive $y$-axis. What is the magnitude of the magnetic field at the point $P(-2 \,mm, 0)$ (in $\,mT$)? (Assume $\frac{\mu_0}{4 \pi} = 10^{-7} \,T \cdot m/A$)

An electron revolves in a circle of radius $0.4 \text{ Å}$ with a speed of $10^6 \text{ m/s}$ in a hydrogen atom. The magnetic field produced at the centre of the orbit due to the motion of the electron (in Tesla) is: $\left[\mu_0 = 4\pi \times 10^{-7} \text{ H/m}, q = 1.6 \times 10^{-19} \text{ C}\right]$

$A$ closely packed coil having $1000$ turns has an average radius of $62.8\,cm$. If the current carried by the wire of the coil is $1\,A$,the value of the magnetic field produced at the centre of the coil will be (permeability of free space $\mu_0 = 4\pi \times 10^{-7}\,T\cdot m/A$) nearly: