A circular coil of radius $$R$$ is carrying a current $$I_1$$ in anti-clockwise sense. A long straight wire is carrying current $$I_2$$ in the negative direction of $$X$$-axis. Both are placed in the same plane and the distance between centre of coil and straight wire is $$d$$. The magnetic field at the centre of coil will be zero for the value of $$d$$ equal to

An $$\alpha$$-particle of energy 10 eV is moving in a circular path in uniform magnetic field. The energy of proton moving in the same path and same magnetic field will be [mass of $$\alpha$$-particle $$=4$$ times mass of proton]

An electron $$(e)$$ is revolving in a circular orbit of radius $$r$$ in hydrogen atom. The angular momentum of the electron is ($$M=$$ magnetic dipole moment associated with it and $$m=$$ mass of electron)

A charged particle is moving in a uniform magnetic field in a circular path of radius $$R$$. When the energy of the particle becomes three times the original, the new radius will be