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### Course: Class 12 Physics (India)>Unit 1

Lesson 3: Coulomb's law and electric force

# Coulomb's law and electric force review

Review your understanding of Coulomb's law and electric forces in this free article aligned to NGSS standards.

## Key terms

TermMeaning
Electric chargeA property of matter that determines the force on the object when placed in an electromagnetic field. Objects can have positive, negative, or neutral charge. Like energy and matter, total electric charge is conserved, and charge cannot be created or destroyed.
$k$The electric force constant, or Coulomb’s constant, which has a value of $9.0\phantom{\rule{0.167em}{0ex}}\text{x}\phantom{\rule{0.167em}{0ex}}{10}^{9}\phantom{\rule{0.167em}{0ex}}\frac{\text{N}\cdot {\text{m}}^{2}}{{\text{C}}^{2}}$.

## Equations

EquationSymbol breakdownMeaning in words
$|{F}_{E}|=k|\frac{{q}_{1}{q}_{2}}{{r}^{2}}|$${F}_{E}$ is electric force, $k$ is the Coulomb’s law constant, ${q}_{1}$ and ${q}_{2}$ are the charges, and $r$ is the distance between the charges.The magnitude of the electric force between ${q}_{1}$ and ${q}_{2}$ is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them. This equation is known as Coulomb’s Law.

## Comparing electric force and gravitational force

Coulomb's law may look somewhat familiar, because it has a lot in common with Newton's law of gravitation:
$\begin{array}{rl}& \begin{array}{rl}|{F}_{E}|& =k|\frac{{q}_{1}{q}_{2}}{{r}^{2}}|\\ & |{F}_{g}|& =G\frac{{m}_{1}{m}_{2}}{{r}^{2}}\end{array}\end{array}$
Like gravitational force, whose magnitude increases with mass, electric force magnitude increases with the magnitude of the charges. Both forces act along the imaginary line joining the objects. Both forces are inversely proportional to the square of the distance between the objects, this is known as the inverse-square law. Also, both forces have proportionality constants. ${F}_{g}$ uses $G$ and ${F}_{E}$ uses $k$, where $k=9.0×{10}^{9}\frac{\text{N}\cdot {\text{m}}^{2}}{{\text{C}}^{2}}$.
A difference between gravitational force and electric force is their relative strengths, related to the ratio of $k$ to $G$. The electrostatic force between an electron and a proton is many orders of magnitude greater than the gravitational force between them.

## Direction of electric force

The electric force ${F}_{E}$ can be either attractive or repulsive. Opposite charges, such as a positive charge and a negative charge, attract each other. Like charges, such as two negative charges or two positive charges, will repel each other.

## What else should I know about Coulomb's law?

• Electric force is inversely proportional to ${r}^{2}$ instead of $r$. As the distance between charges increases, the electric force decreases by a factor of $\frac{1}{{r}^{2}}$. For example, if we double the distance between the two electrons, the repulsive force between them would reduce (because it is inverse), and it would go down by a factor of $4$ instead of $2$ (because of the square).

## Want to join the conversation?

• How do I find the Electric field if the charge is not given but distance is?
• The farthest you could get is to:
Fe =(9*10^9 |q1*q2|)/(whatever your distance is)^2
• is r measured in cm? if not, what unit?
(1 vote)
• in "CGS" system [centi;gram;second] r is measured in centimeters but in "MKS" system [meter;kilo;second] r is measured in meters
• Will an object with more charge have a greater force than the object with a smaller charge?
(1 vote)
• An object with greater charge will exert a greater force on an object than an object with smaller charge would. However, if you consider two charges that exert a force on each other, regardless of the magnitude of charge, both charges will exert an equal force on each other because of Newton's third law.
• What are the laws of attraction?
• Like forces repel one another, and opposites attract. Positive repels positive but attracts negative, and negative repels negative but attracts positive. Its almost kind of like a positive person being the most picked on in school. The negative bullies are using this positive person as a platform, and the positive person always wants to help the negative people "BECOME" positive.
Hope this helps!
(1 vote)
• Excuse me, is there a reason that we need the absolute value for electric force (∣FE∣in the equation) but not for gravitational force?
• We need an absolute value in Electrostatic force and not in gravitational force as, gravity is always attractive whereas electrostatic force is attractive as well as repulsive. So whatever we do, the amount and direction of force is same, but that is not the case in electrostatic force, thus we are using |FE| in the equation.
Hope it helps.
(1 vote)
• how can I tell whether a charge is attractive or repulsive
• Like charges repel.
Unlike charges attract.
• Is there any derivation of relation needed for comparision of Gravtitational and Electrostatic Energy
(1 vote)
• Often in exams, comparison b/w electrostatic and gravitational forces between electron and proton are asked. In that case the ratio b/w Fe and Fg is approx 10^40.
(1 vote)
• k=9.0 \times 10^9 \dfrac{\text N \cdot \text m^2 }{\text C^2}

how do you multiply by this
(1 vote)
• When formatted:
K = 9.0×10^9 (m^2 / C^2)

Or:
K = 9000000000 × (m^2 / C^2)
(1 vote)
• how do I find excess electrons?
(1 vote)
• what would be the equation to figure out the current through repelent and attractive field
(1 vote)
• well, according to the net,
Magnetic field magnitude =
(permeability of free space)*(current magnitude)/2π(distance)
B = μ0/2πr
(1 vote)