A uniform and constant magnetic field $$B=\widehat zB$$ exists in the $$\widehat z$$ direction in vacuum. A particle of mass m with a small charge q is introduced into this region with an initial velocity $$v=\widehat xv_x+\widehat zv_z$$. Given that B, m, q, v_x and v_z are all non-zero, which one of the following describes the eventual trajectory of the particle?

Consider a region of silicon devoid of electrons and holes, with an ionized donor density of $${\mathrm N}_\mathrm d^+=10^{17}\;\mathrm{cm}^{-3}$$. The electric field at x = 0 is 0 V/cm and the electric field at x = L is 50 kV/cm in the positive x direction. Assume that the electric field is zero in the y and z directions at all points.

Given q = 1.6 × 10⁻¹⁹ coulomb, $$\varepsilon$$₀ = 8.85 × 10⁻¹⁴ F/cm, $$\varepsilon$$_r = 11.7 for silicon, the value of L in nm is ________.

The Ebers-Moll model of a BJT is valid

Transistor geometries in a CMOS inverter have been adjusted to meet the requirement for worst case charge and discharge times for driving a load capacitor C. This design is to be converted to that of a NOR circuit in the same technology, so that its worst case charge and discharge times while driving the same capacitor are similar. The channel lengths of all transistors are to be kept unchanged. Which one of the following statements is correct?