Solving for Acceleration of a Charged Particle

Click For Summary
SUMMARY

The discussion focuses on calculating the acceleration of a charged dust particle with a mass of 2.50 mg and a charge of 2.00 µC in a varying electric potential described by the equation V(x) = (2.00 V/m²)x² - (1.00 V/m³)x³. The electric field E is derived as E = -4x + 3x², leading to the force F calculated as F = (2e-6)(-4x + 3x²). The correct acceleration is determined to be approximately 9.856 m/s² after resolving an algebraic error in the initial calculation.

PREREQUISITES
  • Understanding of electric potential and electric fields
  • Familiarity with Newton's second law of motion (F = ma)
  • Basic algebra skills for manipulating equations
  • Knowledge of units for charge and mass in physics
NEXT STEPS
  • Study the relationship between electric potential and electric field in electrostatics
  • Review Newton's laws of motion and their applications in particle dynamics
  • Practice algebraic manipulation of equations in physics problems
  • Explore the effects of varying electric fields on charged particles
USEFUL FOR

Students in physics, particularly those studying electromagnetism and dynamics, as well as educators seeking to clarify concepts related to charged particles in electric fields.

Patdon10
Messages
85
Reaction score
0

Homework Statement


A 2.50-mg dust particle with a charge of 2.00 µC falls at a point x = 2.80 m in a region where the electric potential varies according to
V(x) = (2.00 V/m2)x2 − (1.00 V/m3)x3.
With what acceleration will the particle start moving after it touches down? (Enter the magnitude of the acceleration.)

2. The attempt at a solution

Taking the gradient of V will give you -E. So E = -4x + 3x^2

F = qE ---> F = (2e-6)(-4x+3x^2)
F = (2e-6)(-11.2 + 23.52)
F = 2.464e-5

We also know F = ma
2.464e-5 = (2.5e-6)a
a = 6640.92 m/s^2

This is incorrect. Anyone know what I'm doing wrong?
 
Last edited:
Physics news on Phys.org


Apparently that is right, I just suck at algebra. (2.464*10^-5)/(2.5*10^-6) = 9.856 m/s^2, which is right.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
5K
Replies
4
Views
1K
  • · Replies 25 ·
Replies
25
Views
2K
Replies
13
Views
2K
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
3
Views
3K