Two parallel wires of equal lengths are separated by a distance of $$3 \mathrm{~m}$$ from each other. The currents flowing through $$1^{\text {st }}$$ and $$2^{\text {nd }}$$ wire is $$3 \mathrm{~A}$$ and 4.5 A respectively in opposite directions. The resultant magnetic field at mid point between the wires $$\left(\mu_0=\right.$$ permeability of free space)

Three point charges $$+\mathrm{q},+2 \mathrm{q}$$ and $$+\mathrm{Q}$$ are placed at the three vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of $$Q$$ in terms of $$q$$ is

If a gas is compressed isothermally then the r.m.s. velocity of the molecules

The bob of a simple pendulum of length '$$L$$' has a mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$'. The pendulum is suspended between the plates of a charged parallel plate capacitor. The direction of electric field is shown in figure. The period of oscillations of the simple pendulum is (acceleration due to gravity $$\mathrm{g}>\mathrm{qE} / \mathrm{m}$$ )