An electron moves through a uniform magnetic field $\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T$. At a particular instant of time, the velocity of electron is $\overrightarrow{\mathrm{u}}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}$. If the magnetic force acting on electron is $\vec{F}=5 e\hat kN$, where $e$ is the charge of electron, then the value of $\mathrm{B}_0$ is ____$\mathrm{T}$.

A positively charged particle moving due east enters a region of uniform magnetic field directed vertically upwards. The particle will

An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement$(s)$ is/are true?

$(A)$ They will never come out of the magnetic field region.

$(B)$ They will come out travelling along parallel paths.

$(C)$ They will come out at the same time.

$(D)$ They will come out at different times.

A beam of protons with speed $4 \times 10^{5}\, ms ^{-1}$ enters a uniform magnetic field of $0.3\, T$ at an angle of $60^{\circ}$ to the magnetic field. The pitch of the resulting helical path of protons is close to....$cm$

(Mass of the proton $=1.67 \times 10^{-27}\, kg$, charge of the proton $=1.69 \times 10^{-19}\,C$)

A very high magnetic field is applied to a stationary charge. Then the charge experiences

An electron is travelling in east direction and a magnetic field is applied in upward direction then electron will deflect in