Where Newton’s Third Law doesn’t work

In the last post, I talked about some of the basics of Newton’s three laws of motion.
Reiterating them.
1. The first law is about a body’s reluctance to change its state of motion – If it’s not acted upon by an external force, a body undergoing uniform motion will moving, and a body at rest will remain at rest.
2. The second law is about how a body reacts to a force – The rate of change of momentum of a body is proportional to the force acting on it.
3. The third law states that for every action, there is an equal and opposite reaction.
Here’s an instance, however, where the third law does not apply.
For this bit, you’ll need a little bit of background in electromagnetism.
A moving charge creates a magnetic field around it. The direction of the field is given by the right hand rule. If the thumb of your right hand points along the velocity of a positive charge, your fingers curl along the direction of the field.
Right hand rule
A charge moving in a magnetic field experiences a force that is proportional to the charge of the particle, its velocity, and the magnetic field.
F = qv x B.
The direction of the force experienced by the particle can be given by Fleming’s Left Hand Rule, depicted below. If your forefinger points along the direction of the field a positively charged particle is moving through, and your middle finger in the direction of motion , your thumb points along the direction of the force experienced by the charged particle.
Fleming's left hand rule
Now look at this figure where two positive charges are moving in directions perpendicular to each other.

2016-02-20 06_54_02

The red charged particle (Particle 1) is producing a field B1. The blue particle (Particle 2) is moving through the field upwards. As it does so, it experiences F21, which pushes it to the right side, as shown by the red arrow.

According to Newton’s third law, Particle 1 should also feel a magnetic force F12 to the left, created by Particle 2. However, since the field produced by Particle 2 (B2) is zero at point 1, Particle 1 feels no force acting on it when it is directly underneath Particle 2.

So, F12 = 0.

Newton’s Third Law does not apply.

If you want to dig deeper and understand why momentum is still being conserved in this scenario, you can mull over reference 3. It’s explored there in great detail.

[Note: I am omitting the Coulomb forces the particles are exerting on each other. They are equal and opposite. It’s the magnetic forces that aren’t obeying Newton’s Third Law.]


  1. Fig1:https://www.physics.rutgers.edu/ugrad/227/L15%20Magnetic%20Field%20of%20Currents%20Biot-Savart.pdf
  2. Fig2: http://www.bbc.co.uk/schools/gcsebitesize/science/triple_aqa/keeping_things_moving/the_motor_effect/revision/3/
  3. http://physics.stackexchange.com/questions/138095/newtons-third-law-exceptions


Newton’s Three Laws of Motion – A fun exercise

Let me start with an update on my PhD status. Obvious from the frequency of my blog posts, I have been extremely busy with my projects and coursework. But I am glad to say that, thanks to group mates I can trust and talented lab partners I can rely on when I’m in trouble, things could not have been more productive. And honestly, I don’t mind being under a lot of pressure as long as I am being productive.
Okay, now for the topic of this post. I have been wanting for a long time to write about something that’s very basic in physics – Newton’s Laws.
Before I go into detail, here’s a simple question you can ask your friends. And try to answer it as fast as possible, like, in under ten seconds. Come on, you are a smart guy! You shouldn’t take any more time than that.
While you are asking the question, make sure you contract your arm, and make a throwing motion, providing a visual aid for the innocent victim. If you are lucky, you’ll probably make them give you a wrong answer.
It seems like an easy enough question, but you would be surprised how many get this wrong. Of course, the question lacks a lot of detail. Where in space is the object? How far are the nearest bodies that might exert a force on the object?
The object is not going to slow down. Everyone gets this bit right. There’s no air resistance. So nothing slows the ball down. [Unless your time scale is over millennia and the ball loses its momentum bumping into tiny space particles floating around].
Now, why does the ball not speed up? You did exert a force on it that caused it to accelerate, and as I have established before, there’s nothing there to slow it down, right?
Well, it did accelerate as long as your hand was pushing it forward. But as soon as the ball left your hand, it did not have any force pushing on it anymore. So, it would move in a straight line in a constant speed.
But what about the third law? For every action there is an equal and opposite reaction. So if there is a reaction force, why don’t the two forces cancel each other out and the ball remain at rest?
That’s because the action and the reaction force don’t act on the same body. The reaction force exerted by the ball acted on your hand, and decelerated it, as your biceps tied to pull your hand forward. Since the force by the ball was decelerating your hand, it could not cancel out the force your hand was exerting on the ball.
Sweet. So far we’ve covered high school level physics. But honestly, I have seen Olympiad competitors, engineering students, and even PhD students mess up this simple question. Just needs a little misdirection.
Now, after we have kind of established Newton’s laws and their ‘infallibility’, in my next post, I am going to give you an example where Newton’s third law does not seem to work.

A reason to pursue science as a career

There is a weird old story in Hindu Mythology.
Indradyumna, the son of Bharat, was the greatest man on Earth. It was well known that there was no one to match his “Dharma-Swabhaav”, his righteousness. As a consequence of his good deeds, he ascended to Swarga (Heaven). There, for thousands of years, he enjoyed the limitless luxuries he earned as a consequence of his good deeds. But one day, Indra, the king of the lesser Gods, told him, “O King, you have done immense number of punyaas (good deeds) in your life and as a result you were here for a very long time. The time on earth past so much that now no one remembers any of your good deeds and hence it is time for you to leave heaven”. [Now, why the God king used such a long convoluted way of saying “Time’s up!” escapes me, but that’s pretty much how dialogues in most religious texts go.]
The rest of the story is about Indradyumna’s quest to find the one creature on the planet that remembered his good deeds.

Note to self: Must find out why a lot of famous Hindu are painted blue.

The crux of the story had always struck me as a kid. That even the deeds of the greatest man on earth are great as long as they are remembered.
There are more several ways to be remembered in history. Becoming a great philanthropist like Mother Teresa. Writing great work of literature like Shakespeare.
But for me, a great way to survive would be to make a scientific discovery.
Nothing underpins the impact of making scientific discoveries more than the story of Archimedes.  You know his story about him running in his birthday suit, crying ‘Eureka.’ If you had a good science teacher in your highschool, you might have heard him tell you that it was something about dipping things in water to determine their purity. But you need to delve a little deeper into the story to appreciate the timelessness of an epic scientific figure.

He probably wasn’t bald!

Archimedes died during the siege of Syracuse, during the second Punic War. The name of the war sounds unfamiliar, right? The Punic War took place between the Romans and the Carthaginians. Much like the first and second world wars, the battles saw great strides in scientific discoveries, with all the participants employing cutting edge war machines and military strategy to outclass their opponents. Over a hundred thousand soldiers died in the battles alone, in a war that lasted for seventeen years.
It is one of the battles that shaped human history as we know it. For one thing, if the Carthaginians had won the war, Jesus might not have been born. If you still are not convinced about the epicness of the war, just take a look at the map of the participating nations.
Second Punic War

The original “Second World War”

The fact of the matter is, the Second Punic War was at a time, as significant to human histories as the World Wars are to us. However, we barely remember it.
But we remember Archimedes and his naked run in the streets of Syracuse.
So it is not a far off bet to guess that one day, humanity will forget about the First World War, but remember Maxwell and his equations; we’ll forget about Hitler and the Second World War, but remember Albert Einstein’s theories.
And that is a compelling reason to pursue science as a career, for the remote chance that we might find something that lasts through humanity’s history.
Also, the work hours are nice.
Note: The post was inspired from Professor Evgeni Narimanov’s first lecture in his course ECE60400: Electromagnetic Field Theory. This was undoubtedly one of the best classes I have ever taken.
1. Wikipedia articles – Indradyumna, Second Punic War, List of battles by casualties.
2. Cartoon: https://speechdudes.wordpress.com/tag/archimedes
3. Map:  From the book Atlas of Empires by Peter Davidson.

About this blog

I started this blog as a collection of snapshots of my PhD life, with my short term and long term goals, achievements, ideas and epiphanies, major life events, and basically anything else that is related to my research life.

Here’s a tentative list of what this blog will comprise:

  1. Literature review: I will summarize interesting papers I review in the course of my PhD.
  2. Tutorials on electromagnetism and related problems.
  3. My thoughts on recent events that occur in the scientific community.
  4. Experiences in the cleanroom.
  5. Announcements on upcoming events – conferences, symposia, and workshops.

For tutorials, I will try my best to follow a simplistic approach, keeping jargons and complex mathematics to a minimum. I’ll take the same approach for any journal article I summarize and review.

This is not a complete list, and I am going to keep updating it as I get new ideas for posts.