# Vector differential equation

• abluphoton
In summary, the speaker was assigned a homework to calculate Coulomb's field with moving source charges. They were able to do it for fixed charges but got stuck when trying to do it for charges in motion. They are looking for help with a vector differential equation involving the magnitude of the position vector and acceleration.

## Homework Statement

hi all... i was assigned in my class to do some basic coulomb's field calculation. considering 4 source charges calculating there resultant field anywhere in the space around them. i was able to do that... but later i tried to extend it by giving up the assumption that the source charges are fixed.

i considered 2 point charges and tried to calculate field around them with themselves in motion. i did it fairly well. until i got stuck at a point that seemed like a vector differential equation. will be glad if someone helps me out with this. thanks in advance.

## Homework Equations

(|S|)*(s") = [constant vector]

(|S|) here is the magnitude of the position vector and (s") will be acceleration a vector.

## The Attempt at a Solution

i haven been taught must about this kind of mathematics. I am now looking for an equation of 'S'

im still waiting :(

## 1. What is a vector differential equation?

A vector differential equation is a mathematical equation that describes the relationship between a vector function and its derivatives. It is used to model physical phenomena in fields such as physics, engineering, and economics.

## 2. What are the main components of a vector differential equation?

The main components of a vector differential equation are the vector function, its derivatives, and the independent variables. The vector function is typically denoted by a boldface letter, its derivatives are represented by a dot or prime, and the independent variables are usually denoted by t or x.

## 3. What is the difference between a scalar and a vector differential equation?

A scalar differential equation involves only scalar functions and their derivatives, while a vector differential equation involves vector functions and their derivatives. Scalar differential equations can be solved using basic calculus methods, while vector differential equations often require more advanced techniques such as linear algebra and vector calculus.

## 4. How are vector differential equations used in real-world applications?

Vector differential equations are used to model physical systems and phenomena in various fields such as mechanics, electromagnetics, fluid dynamics, and economics. They are also used in engineering and scientific research to make predictions and solve problems related to these systems and phenomena.

## 5. What are some common methods for solving vector differential equations?

Some common methods for solving vector differential equations include separation of variables, substitution, and variation of parameters. Other more advanced methods include Laplace transforms, power series, and numerical methods such as Euler's method and Runge-Kutta methods.