The magnetic field at the center of current carrying circular loop is $B_1$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is $B_2$. The value of $\frac{B_1}{B_2}$ will be

A wire $X$ of length $50 \mathrm{cm}$ carrying a current of $2 \mathrm{A}$ is placed parallel to a long wire $Y$ of length $5 \mathrm{m}$. The wire $Y$ carries a current of $3 \mathrm{A}$. The distance between two wires is $5 \mathrm{cm}$ and currents flow in the same direction. The force acting on the wire $Y$ is :

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A long solenoid is formed by winding $70$ turns ${\mathrm{cm}}^{-1}$ . If $2.0 \mathrm{A}$ current flows, then the magnetic field produced inside the solenoid is ______________.

$({\mu }_0= 4\mathrm{\pi }\times {10}^{–7} \mathrm{T} \mathrm{m} {\mathrm{A}}^{–1})$