Practice Test 7

An electrostatic sensor is tested near a uniformly charged thin ring of radius $R=0.30\ \text{m}$ carrying total charge $Q=+2.0\ \text{nC}$. The sensor is placed far on the axis at $z=3.0\ \text{m}$ to check the far-field approximation. Consider the setup described above. The field is needed to confirm the ring behaves like a point charge at large distances. Use the ring’s on-axis expression and indicate direction along $\pm\hat{z}$ in N/C.

A MEMS actuator uses a uniformly charged insulating disk (radius $R=0.15,\text{m}$) with surface charge density $\sigma=+4.0,\mu\text{C/m}^2$; a probe at point $P$ lies on the disk’s axis at $z=0.050,\text{m}$ to estimate the axial force. Consider the setup described above. Calculate the electric field at point P on the axis of the charged disk.