Coulomb's law/Electrostatic force says a force's magnitude is proportional to charges' product and inversely proportional to the square of the distance between them.
It calculates the total force between 2 electrical particles at rest. It was first published in 1785 by French physicist and engineer Coulomb, but existed prior. It was crucial to the development electromagnetism theory and, as it helped crucial discussions of total electric charge in particles.
By: Charles Augustin de Coulomb
Published: 1785
[3] Electrical force, as a force is often written in Newton (N) unit and its strength is a vector quantity.
Electrical force's direction depends if charged objects are charged the same or oppositely and by their spatial orientation.
spatial orientation: to understand/relate objects/oneself to each other or giving
Knowing the 2 objects' charge type, the force direction on either of them is found with some reasoning.
E.g. Here, A and B with charge causing them to repel each other. So foce A force directs leftward (away from B) and force B directs rightward (away from A).
C and D have opposite charge, so they attract each other. So force C directs rightward (to object D) and the force D directs leftward (to object C). For the electrical force vector, a way to find the direction is to use the fundamental rules of charge interaction (opposites attract and likes repel) using a little reasoning.
[4] Coulomb (C) is the SI electric charge unit. 1 C is the charge amount carried by 1 A current flowing for 1 s: 1C = 1A x 1s or 6.241 x 10¹⁸ electrons/protons.
1 C is a huge charge in daily cases.
An usual AA battery may carry ~5k C in lifetime, but spread out over hours.
A lightning bolt carries ~15 C charge (but sent in milliseconds).
Hair rubbed by a balloon may hold ~1 microcoulomb (µC) = 10⁻⁶ C.
elementary charge's value 'e' = 1.602176634×10¹⁹ C
As Coulomb is the reciprocal of the elementary charge, 1 C equals:
It's ~6241509074460762607.776 e, so not a elementary charge's integer multiple .
Coulomb used to be defined in force between 2 wires, using ampere's latter definition, as 1 A × 1 s.
The 2019 redefinition of the ampere and other SI base units fixed the numerical value of the elementary charge if written in coulombs thus fixed the coulomb value if expressed as a multiple of the fundamental charge.
Like other SI units, coulomb is modified by prefix added multiplying it by a power of 10.
Note: Common multiples are bolded.
Note: Coulomb’s law problems may use unrealistically big charges.
Textbook problems' (like this pages' exercises) values are exaggerated to simplify math.
True charges are tiny (e.g., nC, µC), so forces between them are small unless distances are microscopic. E.g. Two +1 C charges 1 m apart repel with 9 billion Newtons force (~weight of 10,000 Saturn V rockets!).
1 mole's magnitude of the electrical charge of elementary charges (~ 6.022×1023, the Avogadro number) is known as a faraday unit of charge (closely related to the Faraday constant). 1 faraday is 9.648533212×104 C. In the Avogadro constant (NA)'s terms, 1 C ~1.036×10−5 mol × NA elementary charges.
Every farad of capacitance can hold one coulomb per volt across the capacitor.
One ampere hour equals 3600 C, hence 1 mA⋅h = 3.6 C.
One statcoulomb (statC), the obsolete CGS electrostatic unit of charge (esu), is approximately 3.3356×10−10 C or about one-third of a nanocoulomb.
[1], [2], [3] Coulomb's law equation:
F = electrostatic force
k = Coulomb's constant: ~8.988x10⁹ N⋅m²/C²
q1, q2 = 2 charges' magnitudes
r = distance of center between charges
'k' constant is dependent on the medium charged objects are immersed in. For air, the value is ~9.0 x 10⁹ N • m²/C². If the charged objects are present in water, the value of k can be reduced by as much as 80 factor. Units on 'k' are such that when substituted into the equation the units on charge (Coulombs) and the distance units (meters) cancel, leaving Newton as the force unit.
Coulomb's law equation is an accurate depiction of 2 objects' inbetween force if they act as point charges. A charged conducting sphere interacts with other charged objects as though all of its charge were located at its center. While the charge is uniformly spread across the surface of the sphere, the charge center is said as the sphere's center.
The sphere is a point charge with its excess charge at its center.
As Coulomb's law applies to point charges, distance 'd' is the distance between the centers of charge for both objects (not between surfaces).
q1 and q2 As an object can be charged positively/negatively, q1 and q2 are often written as "+" or "-" values. The charges' sign is representative of whether the object has an excess electrons (a negative object) or a shortage of electrons (a positive object).
It maybe tempting to use "+" and "-" signs in the calculations. While not recommended, no harm results and the result is a "-" value for force is a sign of attractive force and "+" force value means a repulsive force. Mathematically, force value is found as a positive if q1 and q2 are of like charge--either both charge. The force value is negative if q1 and q2 are opposite charge--one is "+" and the other is "-". This is consistent with the concept of oppositely charged objects have an attractive interaction and like charged objects have a repulsive interaction. In the end, if you're thinking conceptually (and not merely mathematically), you would be very able to determine the nature of the force - attractive or repulsive - without the use of "+" and "-" signs in the equation.
[3], [Q2]
E.g. 1# If 2 point charges both have +1.00 Coulomb charge, separated by 1.00 meter, what's the electrical force of repulsion's magnitude between them.
= (8.99 × 10⁹ N⋅m²/C²)*[(|1|*|1||)/1²]
= 8.99 × 10⁹ = F
The repulsion force of two +1 Coulomb charges held a meter apart is 9 billion Newton, a very huge comparing in magnitude to the weight of 2000+ jetliners.
jetliners:
E.g. 2# If 2 point charges both have +2 Coulombs, separated by 0.50 meters, what's the electrical force of repulsion magnitude between them?
= (8.99 × 10⁹ N⋅m²/C²)*[(|2|*|2||)/0.5²]
= (8.99 × 10⁹ N⋅m²/C²)*16
= 143.84x10⁹
The electrical force magnitude is 143.84x10⁹ N (repulsive, as both charges are positive)--a huge force as 1 Coulomb is a huge charge (real-world charges are often in microcoulombs, µC).
[1] Back then we asked "How to predict how strong the attraction/repulsion forces amongst charged particles?"
It isn't til 16th century, did we really analyze these behavior before Coulomb published his law.
[Q1] Flashcard
[Q2] Exercises
[Q3] Quizzes