8. Electric Charges by Integration

by M. Bourne

The force between charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.

So we can write:

`f(x)=(k\ q_1q_2)/x^2`

where q1 and q2 are in coulombs (C), x is in metres, the force is in newtons and k is a constant, k = 9 × 109.

It follows that the work done when electric charges move toward each other (or when they are separated) is given by:

`"Work"=int_a^b(k\ q_1q_2)/(x^2)dx`


An electron has a `1.6 × 10^-19\ "C"` negative charge. How much work is done in separating two electrons from `1.0\ "pm"` to `4.0\ "pm"`?


Search IntMath, blog and Forum

Online Algebra Solver

This algebra solver can solve a wide range of math problems.

Calculus Lessons on DVD


Easy to understand calculus lessons on DVD. See samples before you commit.

More info: Calculus videos

The IntMath Newsletter

Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!

Given name: * required

Family name:

email: * required

See the Interactive Mathematics spam guarantee.