Conservation of Energy and Power

12PHYS - Electricity

Finn Le Sueur

2024

Mahi Tuatahi

  • In an X-ray machine, a heating element releases electrons from a negatively charged plate called the cathode. The electrons are then accelerated by an electric field that exists between the cathode and a positively charged tungsten plate called the anode.
  • The cathode and the anode are connected to a high voltage source of \(20 000 V\). The distance between the cathode and anode plates is \(0.050 m\). The beam of electrons causes X-rays to be released from the anode.
  • Charge on an electron = \(-1.60\times10^{–19}C\)
  • Mass of an electron = \(9.11\times10^{–31}kg\)

a) Calculate the electric field strength between the plates, and state its direction. (A)

Whakatika

\[ \begin{aligned} & V=20000V, d=0.05m && \text{(K)} \newline & E = ? && \text{(U)} \newline & E = \frac{V}{d} && \text{(F)} \newline & E = \frac{20000V}{0.05m} = 400000Vm^{-1} && \text{(S+S)} \newline & \text{Direction: from anode (+ve) to cathode (-ve)} \end{aligned} \]

  • In an X-ray machine, a heating element releases electrons from a negatively charged plate called the cathode. The electrons are then accelerated by an electric field that exists between the cathode and a positively charged tungsten plate called the anode.
  • The cathode and the anode are connected to a high voltage source of \(20,000 V\). The distance between the cathode and anode plates is \(0.050 m\). The beam of electrons causes X-rays to be released from the anode.
  • Charge on an electron = \(-1.60\times10^{–19}C\)
  • Mass of an electron = \(9.11\times10^{–31}kg\)

b) State what type of energy an electron would have at the cathode (negative plate), and what would happen to that energy as the electron moved towards the anode (positive plate). (M)

Whakatika

  • Particle Point of View:
    • Maximum electric potential energy when on the cathode.
    • This electric potential energy is transformed to kinetic energy as it moves away from the cathode.
  • Field Point of View:
    • The field is doing work on the particle, so it loses electric potential energy.
    • This energy is transferred to the particle in the form of kinetic energy
  • In an X-ray machine, a heating element releases electrons from a negatively charged plate called the cathode. The electrons are then accelerated by an electric field that exists between the cathode and a positively charged tungsten plate called the anode.
  • The cathode and the anode are connected to a high voltage source of \(20 000 V\). The distance between the cathode and anode plates is \(0.050 m\). The beam of electrons causes X-rays to be released from the anode.
  • Charge on an electron = \(-1.60\times10^{–19}C\)
  • Mass of an electron = \(9.11\times10^{–31}kg\)

c) Calculate the speed of the electron as it reaches the anode (positive plate). (M)

Whakatika

The field does work on the particle, so it loses energy:

\[ \begin{aligned} & E=400000Vm^{-1}, q=-1.6\times10^{-19}C, d=0.05m && \text{(K)} \newline & E_{p}=W=? && \text{(U)} \newline & E_{p} = W = Fd = Eqd && \text{(F)} \newline & W = 400000Vm^{-1} \times (-1.6\times10^{-19}C) \times 0.05m = -3.2\times10^{-15}J && \text{(S+S)} \end{aligned} \]

Assuming no friction (conservation of energy), all \(E_{p}\) converted to \(E_{k}\):

\[ \begin{aligned} E_{p} &= E_{k} \newline -3.2\times10^{-15}J &= \frac{1}{2}mv^{2} \newline v &= \sqrt{\frac{2\times(-3.2\times10^{-15})}{9.11\times10^{-31}}} = 8.39\times10^{7}ms^{-1} \end{aligned} \]

Styrofoam Balls

  • Use what you now know about conservation of energy to answer Task 3 on your Styrofoam Balls and Electric Fields sheet.