A spherical charged dust particle has a radius of 0.9 μm. The dust particle remains stationary between two parallel plates separated by 15 mm. The potential difference between the plates is 30 V, with the lower plate having a higher potential. The dust particle broke off from a material with a density of 850 kg/m³. Determine the number of extra/deficient electrons on the dust particle.

Two square plates, each with a side of 5.0 cm, are separated by a distance of 2.0 mm. The plates are charged to ±15 nC, creating a uniform electric field between them. A proton is initially at rest near the negative plate. Due to the electric field, it accelerates towards the negative plate. Calculate the speed with which the proton must be shot to just reach the positive plate.

Two electrodes with a separation distance of 3.0 cm have an electric field strength of 3.0 × 10⁴ N/C between them. A proton is released from the negative plate at a 30° angle with respect to the horizontal. Find the maximum initial speed that the proton must have in order to just barely miss hitting the positive plate.

A proton with a kinetic energy of 1.2 × 10  ^-16 J enters a uniform electric field between two parallel plates. If the proton is to turn left, what should be the charge on the plates?

A car battery is connected to a parallel-plate capacitor made of two 10 cm × 10 cm electrodes, with a separation distance of 2.0 mm. The dielectric material between the plates has a breakdown electric field strength of 2.5 × 10⁶ N/C. Determine the number of electrons that must be transferred from one electrode to the other to create a spark in the dielectric material if the dielectric constant is 2.2.

An electrostatic air purifier comprising two horizontal plates each 15 cm × 15 cm is employed to remove smoke particles from the air injected between the plates. The air purifier first ionizes the particles, then passes the air through a region with a uniform electric field, perpendicular to the airflow direction, to deflect the charged particles towards a collection plate. If the smoke particles are charged with 100 extra electrons and the air flows at a speed of 2.5 m/s, what minimum electric field strength is required to deflect the smallest smoke particle by 5.0 mm before it reaches the collection plate? Assume negligible air resistance and gravity. The mass of each smoke particle is 4.0 × 10^-11 g.