Paper 3 Electric Fields Drills

Q1 Charged Particle Deflection

A proton enters a uniform electric field between horizontal plates with horizontal speed $2.4\times 10^6\mathrm{m}{\mathrm{s}}^{-1}$. The plates are $4.0\mathrm{cm}$ long and have field strength $3.0\times 10^4\mathrm{N}{\mathrm{C}}^{-1}$ vertically upward. Take $e=1.60\times 10^{-19}\mathrm{C}$ and $m_p=1.67\times 10^{-27}\mathrm{kg}$.

1. Calculate the vertical acceleration of the proton. [3]
2. Calculate the time spent between the plates. [2]
3. Calculate the vertical deflection on leaving the plates. [3]
4. Explain the path shape. [2]

Q2 Point-Charge Graph Reasoning

A positive point charge has potential $V=kQ/r$ and field magnitude $E=kQ/r^2$.

1. Explain why $V$ is scalar but $\vec{E}$ is vector. [2]
2. Sketch how $V$ and $E$ vary with $r$ for a positive charge. [3]
3. State how the graphs would differ for a negative source charge. [2]