Why is the increase in kinetic energy of the particle after being accelerated

Click For Summary
SUMMARY

The increase in kinetic energy of a particle accelerated by a potential difference of V/2 is quantified as q*V/2, where q represents the charge of the particle. This relationship is derived from the definition of electric potential, which states that potential energy per charge is equal to the electric potential (V). The work done on the charge as it moves through the potential difference is expressed as W = q*V, confirming that the energy gained by the particle is directly proportional to the charge and the potential difference applied.

PREREQUISITES
  • Understanding of electric potential and its relationship to energy (V = Ee/q)
  • Knowledge of electric fields and forces (E = V/d)
  • Familiarity with the concept of work done in physics (W = F*d)
  • Basic principles of charge and its interaction with electric fields
NEXT STEPS
  • Study the derivation of electric potential energy in detail
  • Explore the relationship between electric fields and forces in various configurations
  • Learn about the applications of electric potential in circuit design
  • Investigate the implications of work-energy principles in electrostatics
USEFUL FOR

Students of physics, particularly those focusing on electromagnetism, educators teaching electric potential concepts, and anyone interested in the principles of energy transfer in electric fields.

blueyellow

Homework Statement



what is the increase in kinetic energy of the particle after being accelerated by a potential V/2?

The Attempt at a Solution



The textbook says it is q*V/2 but I just wondered why this is the case
 
Physics news on Phys.org
You probably have two defining formulas for electric potential:
1) potential is the energy per charge, V = Ee/q or Ee = qV
This is the very formula you want explained . . . but it is a definition rather than an explanation.

2) Electric potential causes an electric field between electrodes, E = V/d where d is the distance between the plates. The electric force is F = qE so putting E = F/q into the first formula you have F/q = V/d or F*d = q*V. F*d is the work done as the charge moves through the potential difference so W = q*V. Work done is the energy gained so we have energy = qV.
 

Similar threads

Why does the PE of particles during steam condensation decrease?
  • · Replies 14 ·
Replies
14
Views
1K
Voltage that gives acceleration to relativistic particles
  • · Replies 3 ·
Replies
3
Views
606
Using energy considerations to analyse particle motion
  • · Replies 3 ·
Replies
3
Views
1K
Kinetic Energy of a Cylinder Rolling Without Slipping
  • · Replies 21 ·
Replies
21
Views
5K
Heat added to system increases mass
  • · Replies 12 ·
Replies
12
Views
2K
Can heat flow into a body without increasing the mean kinetic energy?
  • · Replies 1 ·
Replies
1
Views
1K
Is the Photoelectric Effect Proof That Light Is a Particle?
  • · Replies 35 ·
2
Replies
35
Views
4K
Kinetic energy in center of mass reference frame
  • · Replies 3 ·
Replies
3
Views
2K
Why does a fan cool you in a sealed room if it adds heat?
  • · Replies 11 ·
Replies
11
Views
659
Energy of particle in simple harmonic motion
  • · Replies 13 ·
Replies
13
Views
1K