Electric Fields of Charge Distributions Practice Test

A precision ion trap uses a uniformly charged thin ring (insulating) of radius $R=0.12\ \text{m}$ carrying total charge $Q=+3.0\ \text{nC}$. A test point $P$ lies on the ring’s axis a distance $z=0.09\ \text{m}$ from the center. Consider the setup described above. The field is needed to estimate the axial restoring force on ions near the center. Use the standard on-axis ring result and give direction along $\pm\hat{z}$ in N/C.

A charged-particle detector is shielded using a uniformly charged insulating disk of radius $R=0.20\ \text{m}$ with surface charge density $\sigma=+4.0\ \mu\text{C/m}^2$. The disk lies in the $xy$-plane centered at the origin, and point $P$ is on the axis at $z=0.10\ \text{m}$. Consider the setup described above. The field at $P$ is needed to estimate deflection of slow electrons. Use the finite-disk axial field expression and state direction along $\pm\hat{z}$ in N/C.