Solved Example on Coulomb’s Law
Example 1: Charges of magnitude 100 micro coulombs each are located in a vacuum at the corners A, B and C of an equilateral triangle measuring 4 meters on each side. If the charge at A and C are positive and the charge at B negative, what is the magnitude and direction of the total force on the charge at C?
Solution:
Force FCA is applied toward AC and the expression for the FCA is expressed as
[Tex]F_{CA}=\dfrac{qq}{4\pi{\epsilon}_\circ} [/Tex]
Substitute the values in the above expression,
[Tex]F_{CA}=\dfrac{100\times10^{-6}\times100\times10^{-6}}{4\pi\times8.854\times10^{-12}}\\ F_{CA}=5.625\text{ N} [/Tex]
The Force FCB is applied toward CB and the expression for the FCB is expressed as
[Tex]F_{CB}=\dfrac{qq}{4\pi{\epsilon}_\circ} [/Tex]
Substitute the values in the above expression,
[Tex]F_{CB}=\dfrac{100\times10^{-6}\times100\times10^{-6}}{4\pi\times8.854\times10^{-12}}\\ F_{CB}=5.625\text{ N} [/Tex]
Therefore, the two forces are equal in magnitude but in different directions. The angle between them is 120º. The resultant force F is given by,
[Tex]F=\sqrt{F_{CA}^2+F_{CB}^2+2F_{CA}F_{CB}\cos\theta}\\ F=\sqrt{5.625^2+5.625^2+2\times5.625\times5.625\times\cos120^\circ}\\ F=5.625\text{ N} [/Tex]
Example 2: A positive charge of 6×10-6 C is 0.040 m from the second positive charge of 4×10-6 C. Calculate the force between the charges.
Solution:
Given,
First charge q1 = 6×10-6 C.
Second charge q2 = 4×10-6 C.
Distance between the charges r = 0.040 m
k = 9×109
We know that, F = k q1q2 / r2
Substitute the values in the above expression,
F = k q1q2 / r2
F = 9×109×[(6×10-6)× (4×10-6)] / (0.04)2
F= 134.85 N
Example 3: Two-point charges, q1 = +9 μC and q2 = 4 μC are separated by a distance r = 12 cm. What is the magnitude of the electric force?
Solution:
Given,
- k = 8.988 x 109 Nm2C−2
- q1 = +9μC = 9 × 10-6 C
- q2 = +4μC = 4 × 10-6C
- r = 12cm = 0.12m
F = k (q1q2 ∕ r2)
F = (8.9875 × 109 ) [(9x 10-6 ) × (4 x 10-6) / (0.12)2]
F = (8.9875 × 109 ) [36 × 10-12 /0.0144]
F = 22470 N
Electric force between the charges is approximately 22.47 N
For more Problems on Coulomb’s Law
Coulomb’s Law
Coulomb’s Law is defined as a mathematical concept that defines the electric force between charged objects. Columb’s Law states that the force between any two charged particles is directly proportional to the product of the charge but is inversely proportional to the square of the distance between them. Let’s learn about Columb’s law in detail in this article.
Table of Content
- What is Coulomb’s Law?
- History of Coulomb’s Law
- Coulomb’s Law Formula(Scalar Form)
- Coulomb’s Law in Vector Form
- What is 1 Coulomb of Charge?
- Limitations of Coulomb’s Law