Static Electricity — practice questions

Two parallel plates are $5.0$ mm apart with a potential difference of $150$ V across them.

Calculate the electric field strength between them.

Two parallel plates $8.0$ mm apart are connected to a $240$ V supply.

Calculate the field strength between them. The plates are then moved to a separation of $12$ mm with the same supply. Calculate the new field strength and explain why it has changed.

A student sets up two parallel plates connected to a variable power supply, and places a small charged sphere in the gap. They observe that moving the sphere to different positions between the plates does not change the force on it, but moving one plate further away does.

Explain fully why the field between parallel plates is uniform, why the position of the sphere makes no difference, and what would happen to the force if the charge on the sphere were doubled while the plates were unchanged.

A charge of $5.0$ µC is placed in a uniform electric field of strength $2.0 \times 10^4$ N C⁻¹.

Calculate the force on the charge.

A charge of $4.0$ µC is placed between two parallel plates $2.0$ mm apart with $100$ V across them.

Calculate the force on the charge. State and explain the direction of the force if the charge is negative.

A tiny charged oil drop of mass $3.2 \times 10^{-15}$ kg is held stationary between two horizontal parallel plates $6.0$ mm apart connected to a $400$ V supply.

Calculate the charge on the drop, and determine how many excess electrons it carries (electron charge $= 1.6 \times 10^{-19}$ C). Explain fully why the drop must be negatively charged if the upper plate is positive, and explain what would happen if the voltage were then doubled.

A charge of $3.0$ µC moves through a potential difference of $200$ V.

Calculate the energy transferred.

Two parallel plates $5.0$ mm apart have a field strength of $3.0 \times 10^4$ N C⁻¹ between them. A $6.0$ nC charge is moved $3.0$ mm from the positive plate toward the negative plate, and then $4.0$ mm parallel to the plates.

Calculate the total work done on the charge, and explain why the second movement contributes nothing.

Two horizontal parallel plates are $10$ mm apart with $500$ V across them, the lower plate being positive. A proton (charge $+1.6 \times 10^{-19}$ C, mass $1.67 \times 10^{-27}$ kg) is released from rest at the lower plate.

Calculate the energy transferred to the proton and the speed at which it reaches the upper plate. Explain fully what energy changes occur, and explain why the answer would be unchanged if the proton took a longer, curved path between the plates.

A proton (charge $1.6 \times 10^{-19}$ C) is accelerated from rest through a potential difference of $1000$ V.

Calculate the kinetic energy it gains.

An electron (charge $1.6 \times 10^{-19}$ C, mass $9.11 \times 10^{-31}$ kg) is accelerated from rest through a potential difference of $800$ V.

Calculate its final speed, and explain the energy change that takes place.

In an oscilloscope, an electron beam is first accelerated from rest through $2500$ V, then passes horizontally between two deflection plates $50$ mm long which are $10$ mm apart with $80$ V across them.

Calculate the speed of the electrons entering the deflection plates, and their vertical deflection on leaving them. Explain fully why the deflection would be reduced if the accelerating voltage were increased, and identify the assumption you have made about gravity.