If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## AP®︎/College Physics 1

### Course: AP®︎/College Physics 1>Unit 10

Lesson 3: Coulomb's law and electric force

# Coulomb's law and electric force review

NGSS.HS:
HS‑PS2‑4
,
HS‑PS2‑5
,
HS‑PS2.B.1
,
HS‑PS2.B
,
HS‑PS2
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.
kThe electric force constant, or Coulomb’s constant, which has a value of 9, point, 0, start text, x, end text, 10, start superscript, 9, end superscript, start fraction, start text, N, end text, dot, start text, m, end text, squared, divided by, start text, C, end text, squared, end fraction.

## Equations

EquationSymbol breakdownMeaning in words
open vertical bar, F, start subscript, E, end subscript, close vertical bar, equals, k, open vertical bar, start fraction, q, start subscript, 1, end subscript, q, start subscript, 2, end subscript, divided by, r, squared, end fraction, close vertical barF, start subscript, E, end subscript is electric force, k is the Coulomb’s law constant, q, start subscript, 1, end subscript and q, start subscript, 2, end subscript are the charges, and r is the distance between the charges.The magnitude of the electric force between q, start subscript, 1, end subscript and q, start subscript, 2, end subscript 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 {aligned} |{F_E}| &= k \left | \dfrac{q_1 q_2}{r^2} \right | \\\\ |{F_g}| &= G\dfrac{ m_1 m_2}{r^2} \end{aligned}
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, start subscript, g, end subscript uses G and F, start subscript, E, end subscript uses k, where k, equals, 9, point, 0, times, 10, start superscript, 9, end superscript, start fraction, start text, N, end text, dot, start text, m, end text, squared, divided by, start text, C, end text, squared, end fraction.
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, start subscript, E, end subscript 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.
Figure 1. Opposite charges attract each other.
Figure 2. Like charges repel each other.

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

• Electric force is inversely proportional to r, squared instead of r. As the distance between charges increases, the electric force decreases by a factor of start fraction, 1, divided by, r, squared, end fraction. 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?
• 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.
• how can you find k . Sal shows his number in the video for k how did he do that.
• Hello Parv.

We know F = kq1q2/r^2
and k = 1/4πϵ0
To find the value of k, just plug in the values of π (3.1415) and ϵ0 (8.8541 × 10^-12 C^2/Nm^2).

k = 1/4πϵ0
k = 1/4(3.1415)(8.8541 × 10^-12 C^2/Nm^2)
k = 0.00898790 × 10^12 = 8.98790 × 10^9 ≈ 9 × 10^9

There you go!
Hope it helped.
(1 vote)
• What is the direction of force between a proton and an electron?
(1 vote)
• If there are two charges that are ALIKE, they REPEL.
If there are two charges that are DIFFERENT, they attract
.

So, a proton and an electron would attract, because they are different.

A proton with another proton would repel because they have the same charge.

An electron with another electron would also repel, because they have the same charge.

It's like a magnet's south and north poles, but with protons and electrons.
• What are the laws of attraction?
(1 vote)
• 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)
• If both q1 and q2 are positive or negative, how would the equation represent that they are repulsing? Since it takes the absolute value it would always end up as positive, which is attraction. Right?
(1 vote)
• it's just for the magnitude of the force, if you want the proper direction then use the vector form of coulomb's law
(1 vote)
• how do I calculate force if I'm given one charge at an angle say 30 degrees?
(1 vote)
• How would I use thee formula to find the electric field
(1 vote)
• E=F/q

E-Electric field in Newton per Coulomb
F-Force in Newton
q-Charge in Coulomb on which the electrostatic force is exerted
(1 vote)