Electrical Force Formula, SI Unit & Real-Life Examples Explained
Electrical force is the interaction between any two objects that possess electric charge. This force acts as either an attraction or repulsion and is a fundamental concept in understanding both atomic structure and larger-scale electrical phenomena. Like all forces, its effect is guided by Newton's laws of motion, and it can impact the motion, acceleration, or equilibrium of objects based on their charge and position.
Foundations of Electrical Force
An electrical force arises when charged particles—such as electrons and protons—interact. Unlike gravity, which is always attractive, electrical force can be both attractive (between unlike charges) or repulsive (between like charges).
The analysis of electrical forces often makes use of free-body diagrams. These diagrams help in visualizing the different forces acting on an object, such as electric force and gravitational force, allowing for precise calculation of resultant (net) force and predicting the object's motion or static position.
Coulomb’s Law: The Formula for Electrical Force
The electrical force between two point charges is governed by Coulomb’s Law. This law states that the magnitude of the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The formula is:
| Formula | Variables & Meaning |
|---|---|
| F = k × |q₁q₂| / r² |
F = electrical force (N) k = 9 × 109 N·m²/C² (Coulomb's Constant) q₁, q₂ = charge values (Coulombs) r = distance between charges (meters) |
Stepwise Example: Calculating Acceleration with Electric and Gravitational Force
Suppose a 0.90-gram balloon (mass = 0.00090 kg) with a charge of -75 nC is 12 cm above a tube charged to -83 nC. The electric and gravitational forces acting on the balloon can be calculated as follows:
- Compute gravity: Fgrav = m × g = 0.00090 kg × 9.8 m/s² = 8.82 × 10-3 N, down
- Compute electrical force: Convert charge to Coulombs: -75 nC = -75 × 10-9 C;
Distance, r = 0.12 m;
Felect = k × Q₁ × Q₂ / r² = 9 × 109 × (-75 × 10-9) × (-83 × 10-9) / (0.12)² = 3.89 × 10-3 N, up - Determine net force: Fnet = Fgrav (down) + Felect (up) = (8.82 - 3.89) × 10-3 N = 4.93 × 10-3 N, down
- Calculate acceleration: a = Fnet / m = 4.93 × 10-3 N / 0.00090 kg = 5.5 m/s², down
This systematic approach can be used to solve most problems involving a combination of electrical and other forces.
Static Equilibrium: Two Charges in Balance
Imagine two identical balloons, each having a mass of 1.1 grams, suspended on strings of length 2 meters after being negatively charged. If each string makes an angle of 15° with the vertical, it signals a balance between tension, gravity, and electric repulsion.
Using vector components:
- Vertical force (from gravity): Fgrav = 0.0011 kg × 9.8 m/s² = 0.01078 N
- Horizontal (electric) force: Felect = Fgrav × tan(15°) = 0.01078 N × 0.2679 = 0.00289 N
The distance between balloons (d) can be found using trigonometry. First, d/2 = 2.0 × sin(15°) = 0.518 m; thus, d = 1.035 m.
Now, calculate the charge Q using the rearranged Coulomb's law: Q = √[F × d² / k] = √[(0.00289 × (1.035)²)/(9 × 109)] ≈ 5.87 × 10-7 C (negative)
Configurations with More than Two Charges
For systems with three or more charges, calculate the electrical force between pairs independently using Coulomb's law. The net force on any one charge is the vector sum of the individual forces from all other charges.
For example, if four charges are placed at the corners of a square with alternating positive and negative charges, determine each interaction force, note attraction or repulsion, and add the vectors accordingly.
Comparison: Electrical vs. Gravitational Force
| Criterion | Electrical Force | Gravitational Force |
|---|---|---|
| Nature | Attractive & Repulsive | Always Attractive |
| Relative Strength | Much stronger | Much weaker |
| Depends on | Charge | Mass |
| Formula | F = k|q₁q₂| / r² | F = Gm₁m₂ / r² |
Key Applications and Next Steps
- Study Force Between Multiple Charges for vector addition of forces.
- Revise core principles with Electric Charge and Static Electricity.
- Explore real-life cases in Electrostatic Force.
Practice Questions for Mastery
- State and explain Coulomb’s Law with an example calculation.
- Describe what happens when two like-charged objects are suspended and charged, and how you would calculate their repulsive force.
- Find the force and its direction when a 2 μC charge and a -3 μC charge are placed 10 cm apart.
Understanding electrical force and its calculations is essential for Physics. For more advanced learning, practice more problems and explore links on Electrical Force and related topics on Vedantu’s platform.
FAQs on Electrical Force in Physics: Meaning, Formula & Applications
1. What is electrical force?
Electrical force is the attractive or repulsive interaction between any two charged objects. It is a fundamental force of nature described by Coulomb's law and acts along the line joining the charges. The magnitude depends on the amount of charge and the distance between the objects.
2. What is the formula for calculating electrical force?
The formula for electrical force (Coulomb's Law) is:
F = k × |q₁q₂| / r²
where:
• F = electrical force (in Newtons)
• k = Coulomb's constant (8.99 × 109 N·m²/C²)
• q₁, q₂ = charges (in Coulombs)
• r = distance between the charges (in meters)
3. What is the SI unit of electrical force?
The SI unit of electrical force is the Newton (N).
This is the same unit used to measure any force in the International System of Units.
4. Is electrical force always attractive?
No, electrical force can be attractive or repulsive.
• Like charges repel each other.
• Unlike charges attract each other.
This dual nature is a key difference from gravitational force, which is always attractive.
5. What factors affect the magnitude of electrical force between two charges?
The magnitude of the electrical force depends on:
• The product of the magnitudes of the two charges (q₁ and q₂)
• The distance (r) between the charges (— force decreases as distance increases squared)
• The medium between the charges (vacuum/air has maximum force, other media reduce the force)
6. What is another name for electrical force?
Electrical force is also known as electrostatic force or Coulombic force.
These terms are often used interchangeably when referring to the force between stationary electric charges.
7. State Coulomb's Law.
Coulomb's Law states that:
The electrical force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The law is mathematically represented as F = k × |q₁q₂| / r².
8. Give two examples of electrical force in daily life.
Common examples of electrical force in daily life include:
• Static cling of clothes after they are removed from a dryer.
• Rubbing a balloon on hair makes the hair stand up due to static attraction.
These phenomena occur due to the attraction or repulsion of electric charges.
9. How does electrical force compare with gravitational force?
Electrical force is much stronger than gravitational force for subatomic particles:
• Electrical force can attract and repel, and is 1036 times stronger between electrons than gravity.
• Gravitational force is always attractive and comparatively much weaker.
The formulas also differ: F = k|q₁q₂|/r² for electrical, F = Gm₁m₂/r² for gravitational.
10. Can electrical force act at a distance?
Yes, electrical force is a non-contact force and acts at a distance.
Charged objects do not need to physically touch for an electrical force to exist between them. The force acts through the electric field surrounding the charges.
11. What happens to the electrical force if the distance between two charges is doubled?
If the distance between two charges is doubled, the electrical force becomes one-fourth (1/4) its original value.
This is because electrical force is inversely proportional to the square of the distance (F ∝ 1/r²).
12. How do you calculate net electrical force if more than two charges are present?
When more than two charges are present, calculate the force exerted by each charge on the target charge, considering both magnitude and direction, and use vector addition to find the net force.
• Find individual forces using Coulomb’s law.
• Add forces as vectors (tip-to-tail method or component-wise) to get the resultant (net) force.
