In the figure below we have three electric charges

Determine the direction of the force acting on the first charge from the second charge and write the expression for it
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Determine the direction of the force acting on the first charge from the third charge and write the expression for it

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If all three charges are equal in magnitude, what is the direction of the net force acting on the first charge?

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In this simulation we place more than two charges next to each other on a straight line and determine the force acting on a charge and its direction

Solved Example Three point charges are placed at the vertices of a right triangle as shown \[q_1= 2\;µc\;\;\;\;\;\;\;q_2=-3\;µc\;\;\;\;\;\;\;q_3=4\;µc\] and distances between charges are \[r_{12}=0.3\;m\;\;\;\;\;\;\;\;\;\; r_{13}=0.4\;m\] Calculate the electric force on the first charge.
Solution
\[Fe_{21}=K\frac {q_1.q_2}{r_{12}^2}=9×10^9×\frac {2×10^{-6}×3×10^{-6}}{0.3^2}=0.6 N \] \[Fe_{31}=K\frac {q_1.q_3}{r_{13}^2}=9×10^9×\frac {2×10^{-6}×4×10^{-6}}{0.2^2}=1.8 N \] \[F_{net}=\sqrt {F_{21}^2+F_{31}^2}=\sqrt {0.6^2+1.8^2}=1.9 N \] Direction \[𝜃=tan^{-1}\frac {Fe_{21}}{Fe_{31}}=tan^{-1}\frac {0.6}{1.8}=18.4^0\]

Electric Force Between Three Charges

Coulomb's Law:

Force between two charges: \[F=K.\frac{q_1.q_2}{r^2}\]

Method to determine resultant force:

1. Determine direction of force between each pair (repulsion ←← or attraction →←)
2. Calculate magnitude of force between each pair using the law
3. Add forces vectorially according to their directions

Important Notes:

• Sign of charges is taken into account (attraction/repulsion)
• Distances are calculated using Pythagorean theorem if needed
• Direction depends on nature of charges:

  Charge type	Force direction
  Like charges	Repulsion
  Unlike charges	Attraction

Practical Applications

1. Electrostatic forces are used to collect emissions in chimneys

   Electrostatic precipitators are used in factories to purify smoke and particles from industrial emissions.

   Exhaust gases pass through a chamber containing electrodes that charge suspended particles with a positive charge.

   Charged particles are attracted to collection plates with negative charge where they adhere.

   Plates are cleaned periodically to remove accumulated particles.

   This technology is very effective in removing fine particles up to 99% in some applications.

2. Charging paint droplets and car painting

   Static electricity is used in car painting to provide even and organized paint application.

   Paint particles are given a positive electric charge while the car body is given a negative charge.

   Electrostatic attraction draws paint particles to all surfaces of the car, even corners and hidden areas.

   This technique reduces paint waste and provides better coverage with a more uniform coat.

3. Laser printers

   Laser printers rely on principles of static electricity in their operation.

   The printer contains a drum charged with a uniform electrostatic charge.

   The laser removes charge from areas where the image or text should appear.

   Toner powder (charged with opposite charge) adheres to the charged areas on the drum.

   The toner is then transferred to the paper (given a stronger charge) and fused with heat.

4. Food packaging

   Static electricity is used in food packaging to create airtight seals.

   An electric charge is applied to plastic or wrap to make it adhere better to the product or to the other layer of wrapping.

   This technique helps protect food from spoilage and extends its shelf life.

   It is also used in packaging food with clear nylon where the plastic layer adheres evenly to the product.

Comparison between Electrostatic Force and Gravitational Force