The current passing through a conducting loop in the form of equilateral triangle of side $4 \sqrt{3} \mathrm{~cm}$ is 2 A . The magnetic field at its centroid is $\alpha \times 10^{-5} \mathrm{~T}$. The value of $\alpha$ is $\_\_\_\_$ .

(Given : $\mu_{\mathrm{o}}=4 \pi \times 10^{-7}$ SI units)

An infinitely long straight wire carrying current $I$ is bent in a planar shape as shown in the diagram. The radius of the circular part is $r$. The magnetic field at the centre $O$ of the circular loop is :

A current carrying solenoid is placed vertically and a particle of mass $m$ with charge $Q$ is released from rest. The particle moves along the axis of solenoid. If $g$ is acceleration due to gravity then the acceleration (a) of the charged particle will satisfy :

Figure shows a current carrying square loop ABCD of edge length is ‘a’ lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is