If '$$E$$' and '$$L$$' denote the magnitude of total energy and angular momentum of revolving electron in $$\mathrm{n}^{\text {th }}$$ Bohr orbit, then

The magnetic field inside a current carrying toroidal solenoid is $$0.2 \mathrm{~mT}$$. What is the magnetic field inside the toroid if the current through it is tripled and radius is made $$\frac{1}{3}^{\text {rd}}$$ ?

A body of mass '$$m$$' performs linear S.H.M. given by equation $$x=P \sin \omega t+Q \sin \left(\omega t+\frac{\pi}{2}\right)$$. The total energy of the particle at any instant is

Two particles $$A$$ and $$B$$ having same mass have charge $$+q$$ and $$+4 q$$ respectively. When they are allowed to fall from rest through same electric potential difference, the ratio of their speeds '$$V_A$$' to '$$\mathrm{V}_{\mathrm{B}}$$' will become