Electric Fields in Capacitors Practice Problems

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.

A parallel plate capacitor has plates with dimensions 15 cm × 15 cm and a charge of ±60 nC as depicted in the figure. A 2.5 g cube hangs freely within the capacitor and is attracted to one of the plates. Determine the charge on the cube.

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.

An electrostatic spray painting system forms a uniform coating by directing charged paint droplets vertically with deflecting electrodes while the nozzle moves horizontally. It forms 25-μm-radius droplets, charges them with 1,000,000 electrons, and propels them at 25 m/s. These droplets traverse between two parallel electrodes, 8.0 mm long and 5.0 mm wide, spaced 1.5 mm apart. The electrodes are 3.0 cm away from the surface. To achieve the desired 8.0 mm coating height, the droplets must be deflected 4.0 mm. What electric field strength is needed for this deflection? The paint, a mix of pigment in a solvent, has a 1200 kg/m³ density.

An electron moves horizontally eastward at 7.20 × 10⁶ m/s. Determine the least electric field strength and direction of an electric field that slows the electron at a constant rate to a complete stop within 3.6 cm.

An electron moves horizontally to the east with a velocity of 2.40 × 10⁶ m/s. The electron enters an electric field that slows it uniformly. It comes to rest after covering 2.5 cm in the electric field. Determine the time taken by the electron to stop from the moment it enters the electric field.

A hydrogen ion (essentially a proton) has a horizontal velocity of 2.40 × 10⁶ m/s to the east. If the ion should stop within 4.0 cm inside an electric field, determine the minimum electric field strength and direction of an electric field that slows the ion uniformly.

Calculate the time taken by a hydrogen ion (H⁺) that is initially at rest in a uniform electric field of magnitude E = 1.25 kN/C to cover 50.0 mm. 

An electron gun releases an electron in the positive x-direction into a constant electric field of 2.3 × 10⁴ N/C. The electric field is directed in the negative y-direction. The electron undergoes a vertical displacement of 2.1 cm after having moved 0.82 cm horizontally. Calculate the electron's initial speed.

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.

A tiny particle of mass 5 × 10^-15 kg and a charge of 4 nC is accelerated from rest between two oppositely charged flat parallel sheets where there is a constant horizontal electric field of +280 N/C. The two sheets are separated by a distance of 5.0 mm. Find the speed of the particle 1 μs after being released.

Two infinite parallel sheets of opposite charge are separated by 25.0 cm. An electron is released from rest at the surface of the negative sheet and reaches the positive sheet 3 μs later. What is the magnitude of the electric field (E) between the two sheets?

Two equal and large metallic sheets are charged with opposite charges to the same magnitude. The separation of the sheets is 54 mm. Determine the magnitude of the electric field between the two plates given that the surface charge density on each sheet is 20.2 nC/m².

Two oppositely charged parallel plates are separated by a distance of 1.0 cm. A small charged object with a charge of +2e, where e is the elementary charge and mass of 6.68 × 10^-27 kg, is placed initially at rest at a point midway between the plates and has reached 3.1 × 10⁵ m/s just before it hits the negative plate. What is the electric field between the plates?