capacitators and ev

Introduction to Capacitors

  • Topic overview:

    • Discussion on capacitors

    • Introduction to a new unit for energy: electron volt (eV)

Electron Volt (eV)

  • Definition:

    • An electron volt (eV) is the kinetic energy gained by an electron when it is accelerated through a potential difference of one volt. It's a unit of energy.

  • Conversion:

    • 1 eV = 1.6 \times 10^{-19} joules

Relevance of eV in Medical Fields

  • Connection to medical applications:

    • The principle of charged particles moving through a potential difference is how X-rays are generated.

    • In radiology, the energy gained by electrons transformed into X-rays is frequently expressed in eV.

    • Clinical settings often utilize eV to discuss the energy of various X-ray emissions.

Example Problem

  • Problem statement:

    • Calculate the work done by the electric field in moving a proton from +125 volts to -45 volts. Answer should be in both joules and eV.

  • Calculation:

    • Work done = (Final potential - Initial potential) × charge;

    • W = (125 - (-45)) \times e = (125 + 45) \times e = 170 \times e where e is the charge of an electron.

  • Results:

    • Work done: 170e eV; Convert 170e eV to joules using conversion factor.

Parallel Plate Capacitors

  • Definition:

    • A parallel plate capacitor consists of two parallel plates made of conducting material, one carrying positive charge and the other carrying negative charge.

  • Important characteristics:

    • Potential difference between plates is denoted as \Delta V_c (potential difference across the capacitor).

    • Generates a uniform electric field between the plates.

    • The electric field points from the positive plate to the negative plate (direction of decreasing potential).

Key Variables in Parallel Plate Capacitors

  • Charge on plates:

    • Positive charge is denoted as Q and negative charge as -Q.

  • Distance variables:

    • x: position in between the plates.

    • d: total separation distance between the plates.

Electric Field and Potential Calculations

  • Electric field ( E) in parallel plate capacitors:

    • E = \frac{\Delta V_c}{d} where:

    • \Delta V_c is the potential difference across the capacitor.

    • d is the distance between the plates.

    • Electricity field magnitude also given by:

    • E = \frac{Q}{\varepsilon_0 A}

      • Where A is the plate area and \varepsilon_0 = 8.85 \times 10^{-12} \text{ F/m} (constant).

  • Electric potential at position x:

    • V(x) = E \times x

Example Problem for Electric Potential and Electric Field

  • Given:

    • Electric field: E = 1600 \text{ V/m}

    • Distance between plates: 0.0075 m

  • Objective:

    • Find potential difference (\Delta V_c).

  • Approach:

    • Use the formula \Delta V_c = E \times d to find:

    • \Delta V_c = 1600 \times 0.0075 = 12 \text{ V}.

Relationships between Variables

  • Notation of different electric potentials:

    • V is the potential at a specific point between plates, and \Delta V_c is the overall potential difference across the capacitor.

  • Commonly assumed values in parallel plate capacitors:

    • V = 0 at the negative plate.

    • V = V_c at the positive plate

Capacitance

  • Definition:

    • Capacitance C measures an object’s ability to store electrical charge.

  • Formula relating charge, potential difference, and capacitance:

    • C = \frac{Q}{\Delta V_c}

    • C: Capacitance measured in farads (F)

    • Q: Charge in coulombs (C)

    • \Delta V_c: Potential difference in volts (V)

  • SI Unit of Capacitance:

    • Farad (
      F) defined as 1 \text{ F} = 1 \text{ C/V}

Charging a Capacitor

  • Charging mechanism:

    • Capacitors are charged by connecting to a battery, which acts as a charge pump.

    • Electrons move from one plate to accumulate charge on the other plate until equilibrium is reached where potential difference = battery voltage.

    • Important note:

    • Direction of charge movement is conventionally described as the movement of positive charges, although it’s the electrons (negative charges) that actually move.

Summary of Key Formulas

  • Electric field in a parallel plate capacitor:

    • E = \frac{\Delta V_c}{d}

  • Relationship between charge, capacitance:

    • C = \frac{Q}{\Delta V_c}

  • Capacitance of a parallel plate capacitor:

    • C = \frac{\varepsilon_0 A}{d}