# Solving for Acceleration of a Charged Particle

• Patdon10
In summary, a 2.50-mg dust particle with a charge of 2.00 µC falls at a point x = 2.80 m in a region with varying electric potential. By taking the gradient of V, we get the equation E = -4x + 3x^2, where E is the electric field. Using the formula F = qE, we can find the force acting on the particle, which is equal to 2.464e-5. This force can also be expressed as F = ma, allowing us to solve for the acceleration, which is 6640.92 m/s^2. However, after realizing a mistake in algebra, the correct acceleration is found to be
Patdon10

## 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:

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.

## What is the acceleration of a charged particle?

The acceleration of a charged particle is the rate of change of its velocity with respect to time. It is a vector quantity that describes the change in velocity of a charged particle in a specific direction.

## What factors affect the acceleration of a charged particle?

The acceleration of a charged particle is affected by the strength of the electric field, the mass of the particle, and the magnitude and direction of the particle's charge. The presence of other charged particles in the vicinity can also affect the acceleration.

## How do you solve for the acceleration of a charged particle?

To solve for the acceleration of a charged particle, you can use the equation a = qE/m, where a is the acceleration, q is the charge of the particle, E is the electric field strength, and m is the mass of the particle.

## What is the unit of measurement for acceleration of a charged particle?

The unit of measurement for acceleration of a charged particle is meters per second squared (m/s²). This is the same unit used to measure acceleration in general.

## Can the acceleration of a charged particle be negative?

Yes, the acceleration of a charged particle can be negative if the direction of the electric field and the particle's charge are opposite. This indicates that the charged particle is slowing down or changing direction due to the electric field.

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