List of top Sensors and Industrial Instrumentation Questions on Electromagnetism

An air filled parallel plate electrostatic actuator is shown in the figure. The area of each capacitor plate is $100 \mu m \times 100 \mu m$. The distance between the plates $d_0 = 1 \mu m$ when both the capacitor charge and spring restoring force are zero as shown in Figure (a). A linear spring of constant $k = 0.01 N/m$ is connected to the movable plate. When charge is supplied to the capacitor using a current source, the top plate moves as shown in Figure (b). The magnitude of minimum charge (Q) required to momentarily close the gap between the plates is ________ $\times 10^{-14} C$ (rounded off to two decimal places). Note: Assume a full range of motion is possible for the top plate and there is no fringe capacitance. The permittivity of free space is $\epsilon_0 = 8.85 \times 10^{-12} F/m$ and relative permittivity of air ($\epsilon_r$) is 1.

 

An air filled parallel plate electrostatic actuator is shown in the figure. The area of each capacitor plate is $100 \mu m \times 100 \mu m$. The distance between the plates $d_0 = 1 \mu m$ when both the capacitor charge and spring restoring force are zero as shown in Figure (a). A linear spring of constant $k = 0.01 N/m$ is connected to the movable plate. When charge is supplied to the capacitor using a current source, the top plate moves as shown in Figure (b). The magnitude of minimum charge (Q) required to momentarily close the gap between the plates is ________ $\times 10^{-14}$ C (rounded off to two decimal places).
Note: Assume a full range of motion is possible for the top plate and there is no fringe capacitance. The permittivity of free space is $\epsilon_0 = 8.85 \times 10^{-12}$ F/m and relative permittivity of air ($\epsilon_r$) is 1.

A 60 V DC source with an internal resistance \(R_{int} = 0.5 \, \Omega\) is connected through a switch to a pair of infinitely long rails separated by \(l = 1\) m as shown in the figure. The rails are placed in a constant, uniform magnetic field of flux density \(B = 0.5\) T, directed into the page. A conducting bar placed on these rails is free to move. At the instant of closing the switch, the force induced on the bar is