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.

A potential difference of $600\mathrm{V}$ is applied across the plates of a parallel plate condenser. The separation between the plates is $3\mathrm{mm}$. An electron projected vertically, parallel to the plates, with a velocity of $2\times {10}^6 {\mathrm{ms}}^{-1}$ moves undeflected between the plates. Find the magnitude of the magnetic field in the region between the condenser plates.

(Neglect the edge effects). (Charge of the electron $=1.6\times {10}^{-19}\mathrm{C}$) 

An arc of a circular loop of radius $R$ is kept in the horizontal plane and a constant magnetic field $B$ is applied in the vertical direction as shown in the figure. If the arc carries current I then find the force (in $N$) on the arc.

Use $I=\sqrt{2}\mathrm{A}, R=1\mathrm{m}$ and $B=2.5\mathrm{T}$