The capacitance of a parallel plate capacitor with air as medium is $$3 \mu \mathrm{F}$$. With the introduction of a dielectric medium between the plates, the capacitance becomes $$15 \mu \mathrm{F}$$. The permittivity of the medium in $$\mathrm{SI}$$ unit is $$[\varepsilon_0=8.85 \times 10^{-12} \mathrm{SI}$$ unit]

The mass of earth is 81 times the mass of the moon and the distance between their centres is $$R$$. The distance from the centre of the earth, where gravitational force will be zero is

A coil of $$n$$ turns and resistance $$R \Omega$$ is connected in series with a resistance $$\frac{R}{2}$$. The combination is moved for time $$t$$ second through magnetic flux $$\phi_1$$ to $$\phi_2$$. The induced current in the circuit is

Two identical bar magnets each of magnetic moment $$M$$, separated by some distance are kept perpendicular to each other. The magnetic induction at a point at the same distance $$d$$ from the centre of magnets, is ($$\mu_0=$$ permeability of free space)