A uniform magnetic field acts at right angles to the direction of motion of electrons. As a result, the electron moves in a circular path of radius $2\, cm$. If the speed of the electrons is doubled, then the radius of the circular path will be.....$cm$

A particle of charge $16\times10^{-16}\, C$ moving with velocity $10\, ms^{-1}$ along $x-$ axis enters a region where magnetic field of induction $\vec B$ is along the $y-$ axis and an electric field of magnitude $10^4\, Vm^{-1}$ is along the negative $z-$ axis. If the charged particle continues moving along $x-$ axis, the magnitude of $\vec B$ is

A proton moving with a velocity, $2.5 \times {10^7}\,m/s$, enters a magnetic field of intensity $2.5\,T$ making an angle ${30^o}$ with the magnetic field. The force on the proton is

An electron having kinetic energy $T$ is moving in a circular orbit of radius $R$ perpendicular to a uniform magnetic induction $\vec B$ . If kinetic energy is doubled and magnetic induction tripled, the radius will become 

Write Lorentz force equation.

A particle of charge per unit mass $\alpha$ is released from origin with a velocity $\bar{v}=v_0 \vec{i}$ in a uniform magnetic field $\bar{B}=-B_0 \hat{k}$. If the particle passes through $(0, y, 0)$ then $y$ is equal to