IB DP Physics: HL复习笔记10.2.8 Forces on Charges & Masses

Forces on Charges & Masses

  • The electric field strength equation can be rearranged for the force F on a charge Q in an electric field E:
  • Where:
    • F = electrostatic force on the charge (N)
    • Q = charge (C)
    • E = electric field strength (N C-1)
  • The direction of the force is determined by the charge:
    • If the charge is positive (+) the force is in the same direction as the E field
    • If the charge is negative (-) the force is in the opposite direction to the E field
  • The force on the charge will cause the charged particle to accelerate if its in the same direction as the E field, or decelerate if in the opposite

18.1-Force-on-charge-in-E-field

An electric field strength E exerts a force F on a charge +Q in a uniform electric field

  • Note: the force will always be parallel to the electric field lines

Motion of Charged Particles

  • A charged particle in an electric field will experience a force on it that will cause it to move
  • If a charged particle remains still in a uniform electric field, it will move parallel to the electric field lines (along or against the field lines depending on its charge)
  • If a charged particle is in motion through a uniform electric field (e.g. between two charged parallel plates), it will experience a constant electric force and travel in a parabolic trajectory

18.1-Parabolic-trajectory

The parabolic path of charged particles in a uniform electric field

  • The direction of the parabola will depend on the charge of the particle
    • A positive charge will be deflected towards the negative plate
    • A negative charge will be deflected towards the positive plate
  • The force on the particle is the same at all points and is always in the same direction
  • Note: an uncharged particle, such as a neutron experiences no force in an electric field and will therefore travel straight through the plates undeflected
  • The amount of deflection depends on the following properties of the particles:
    • Mass – the greater the mass, the smaller the deflection and vice versa
    • Charge – the greater the magnitude of the charge of the particle, the greater the deflection and vice versa
    • Speed – the greater the speed of the particle, the smaller the deflection and vice versa

Worked Example

A single proton travelling with a constant horizontal velocity enters a uniform electric field between two parallel charged plates.The diagram shows the path taken by the proton.

18.1-WE-Motion-of-Charges-Particles-proton-trajectory

Draw the path taken by a boron nucleus that enters the electric field at the same point and with the same velocity as the proton.Atomic number of boron = 5

Mass number of boron = 11

Step 1: Compare the charge of the boron nucleus to the proton

    • Boron has 5 protons, meaning it has a charge 5 × greater than the proton
    • The force on boron will therefore be 5 × greater than on the proton

    Step 2: Compare the mass of the boron nucleus to the proton

    • The boron nucleus has a mass of 11 nucleons meaning its mass is 11 × greater than the proton
    • The boron nucleus will therefore be less deflected than the proton

    Step 3: Draw the trajectory of the boron nucleus

    • Since the mass comparison is much greater than the charge comparison, the boron nucleus will be much less deflected than the proton
    • The nucleus is positively charged since the neutrons in the nucleus have no charge
      • Therefore, the shape of the path will be the same as the proton

18.1.5_Motion_of_Charged_Particles_Worked_example_Boron_trajectory_1

 

 

 

 

 

 

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