Force on Moving Charge — Prelims Questions

A proton enters a uniform magnetic field $\vec{B} = 0.2\,\hat{k}\,\text{T}$ with a velocity $\vec{v} = (3\,\hat{i} + 4\,\hat{j}) \times 10^6\,\text{m/s}$. What is the magnitude of the magnetic force on the proton? (Charge of proton $e = 1.6 \times 10^{-19}\,\text{C}$)

An electron is moving with a velocity of $5 \times 10^6\,\text{m/s}$ along the positive x-axis. It enters a uniform magnetic field of $0.5\,\text{T}$ directed along the positive y-axis. What is the direction of the magnetic force on the electron?

A proton (mass $m_p = 1.67 \times 10^{-27}\,\text{kg}$, charge $e = 1.6 \times 10^{-19}\,\text{C}$) enters a uniform magnetic field of $0.8\,\text{T}$ perpendicularly with a speed of $3 \times 10^7\,\text{m/s}$. What is the radius of its circular path?

A charged particle is projected into a region where both electric field $\vec{E}$ and magnetic field $\vec{B}$ are present. If the particle passes undeflected, which of the following statements is true?

A charged particle moves in a uniform magnetic field. Which of the following quantities remains constant?

A particle of charge $q$ and mass $m$ is projected with velocity $\vec{v}$ into a region containing a uniform magnetic field $\vec{B}$. If the velocity vector makes an angle $\theta$ with the magnetic field, what is the pitch of the helical path followed by the particle?