Calculate $B\times {10}^5$, where $B$ is magnetic field (in SI unit) at point '$O$' of current distribution, where $I=3.14\mathrm{A}$ and $r=6.28\mathrm{cm}$

 

Six wires of current $I_1=1\mathrm{A}, I_2=2\mathrm{A}, I_3=3\mathrm{A},I_4=1\mathrm{A},I_5=5\mathrm{A}$ and $I_6=4\mathrm{A}$ cut the page perpendicularly at the points $1,2,3,4$ and $6$ respectively as shown in the figure. Find the magnitude of the integral $\frac{\oint \overrightarrow{B}·d\overrightarrow{l}}{{\mu }_0}$ around the closed path.

Calculate magnetic moment (in SI unit) of shown system. (Use$q=6 \mathrm{C}, \omega =10 \mathrm{rad} {\sec }^{-1}$ and $l=1 \mathrm{m}$)

A straight wire of length $l$ carries current $I$ is moulded in the form of semicircular loop then its magnetic moment (in SI unit) is $x\times {10}^{-1}$, where $I=2\mathrm{A}$ and $l=4\mathrm{m}$. Write the value of $x$ to the nearest integer.

A Closely-wound solenoid of $1000$ turns and area of cross-section $2\times {10}^{-4}{\mathrm{m}}^2$ carries a current of $2.0$ ampere. It is placed with its horizontal axis at $30°$ with the direction of a uniform horizontal magnetic field of $0.16\mathrm{T}$ as shown in figure. What is the value of $\tau \times {10}^2$, where $\tau$ is torque (in SI unit) experienced by the solenoid?

A square current carrying loop made of thin wire and having a mass $m=10 \mathrm{g}$ can rotate without friction with respect to the vertical axis $O{O}_1$, passing through the centre of the loop at the right angles to two opposite sides of the loop. The loop is placed in a homogeneous magnetic field with an induction $B={10}^{-1} \mathrm{T}$ directed at right angles to the plane of the drawing. A current $I=2\mathrm{A}$ is flowing in the loop. The period(in second) of small oscillations that the loop performers about its position of stable equilibrium is $T$, write the value of $10T$ to the nearest integer.