Chapter Contents

• Applications of Integration
• 1. Applications of the Indefinite Integral
• 2. Area Under a Curve
• 3. Area Between 2 Curves
• 4. Volume of Solid of Revolution
• 5. Centroid of an Area
• 6. Moments of Inertia
• 7. Work by a Variable Force
• 8. Electric Charges
• 9. Average Value
• Head Injury Criterion
• a. Normal Braking
• b. Crash Tests
• c. Data
• d. Severity Index
• e. Head Injury Criterion
• f. Modelling the HIC
• g. Conclusions
• 10. Force by Liquid Pressure
• 11. Arc Length of a Curve
• 12. Arc Length of a Curve in Parametric or Polar Coordinates
• Applications of Integration Problem Solver

• Comments, Questions?

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8. Electric Charges

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`

Example

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"`?

Answer