Lorentz Force — Prelims Questions

A proton enters a uniform magnetic field of $0.5,\text{T}$ with a velocity of $4 \times 10^5,\text{m/s}$ at an angle of $30^circ$ with the field. Calculate the magnitude of the magnetic force experienced by the proton. (Given: charge of proton $e = 1.6 \times 10^{-19},\text{C}$)

An electron moves in a uniform magnetic field $\vec{B} = B_0 \hat{k}$. If its velocity is $\vec{v} = v_x \hat{i} + v_y \hat{j}$, what is the direction of the magnetic force on the electron?

A charged particle moves in a circular path of radius $R$ in a uniform magnetic field. If its speed is doubled and the magnetic field strength is halved, what will be the new radius of its circular path?

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

An electron is moving with a velocity $\vec{v} = (2\hat{i} + 3\hat{j}) \times 10^6,\text{m/s}$ in a magnetic field $\vec{B} = (0.5\hat{k}),\text{T}$. What is the magnetic force on the electron? (Charge of electron $e = -1.6 \times 10^{-19},\text{C}$)

Which of the following statements about the magnetic Lorentz force is INCORRECT?

A charged particle with charge $q$ and mass $m$ is projected into a uniform magnetic field $\vec{B}$ with a velocity $\vec{v}$ such that $\vec{v}$ makes an angle $\phi$ with $\vec{B}$. Describe the path of the particle.