A solenoid of length $$0.4 \mathrm{~m}$$ and having 500 turns of wire carries a current $$3 \mathrm{~A}$$. A thin coil having 10 turns of wire and radius $$0.1 \mathrm{~m}$$ carries current $$0.4 \mathrm{~A}$$. the torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid is $$\left(\mu_0=4 \pi \times 10^{-7}\right.$$ SI units, $$\left.\pi^2=10\right)\left(\sin 90^{\circ}=1\right)$$

Two circular coils made from same wire but radius of $$1^{\text {st }}$$ coil is twice that of $$2^{\text {nd }}$$ coil. If magnetic field at their centres is same then ratio of potential difference applied across them is ($$1^{\text {st }}$$ to $$2^{\text {nd }}$$ coil)

The ratio of magnetic field at the centre of the current carrying circular loop and magnetic moment is $$X$$. When both the current and radius are doubled, then the ratio will be

A circular current carrying coil has radius $$R$$. The magnetic induction at the centre of the coil is $$B_C$$. The magnetic induction of the coil at a distance $$\sqrt{3} R$$ from the centre along the axis is $$B_A$$. The ratio $$B_A: B_C$$ is