Sunday, January 30, 2011

The Magnetar Credit Card Swipe

Ned Flanders' credit card doesn't satisfy the Luhn checksum,
but could probably still be erased by a magnetar. 
Hello, Internet!  Today I'd like to talk about the Magnetar Credit Card Swipe.  Sounds like some sinister short on a derivatives deal, doesn't it?  Well, no need to worry, we don't deal with scary things like that here.  Instead, we are going to talk about a super-magnetized neutron star speeding past Earth.

A while ago I heard that a magnetar can erase all the world's credit cards from half the distance to the moon.  I did a little research and it seems like this is the go-to "fun fact" about magnetars.  Almost every time they are brought up in a popular science article, their credit card-erasing prowess is sure to get a mention.  So let's check it out!


First things first, though.  What the heck is a magnetar [1]?  Well, "magnetar" is just a spiffy name for a particular flavor of neutron star.  Now, neutron stars are already pretty extreme objects.  They've got a little more than the mass of the sun squished down to the size of a big city with a central density over 10 trillion times greater than lead.    

Dipolar magnetic field
What makes magnetars truly name-worthy (and more extreme than Doritos and Mountain Dew at the X-Games) is the fact that they have strong magnetic fields.  And when I say strong, I mean really strong.  Taking the magnetic field to be dipolar (like the Earth's, see figure), the field at the poles of a magnetar can be as high as 10^15 gauss [2].  For comparison, the magnetic field of the Earth is about half a gauss and the big magnets used in MRIs are about 10^4 gauss.  So we're talking about some big fields!

Looking up the specs for a typical credit card, it looks like most take about 1000 gauss to erase.  And now we can get started.

I always forget the exact form of the magnetic field of a dipole, but Jackson doesn't.  He tells me that it is

\[ \vec{B}\left(\vec{r}\right) = \frac{3\vec{n}\left(\vec{n}\cdot\vec{m}\right) - \vec{m}}{|\vec{r} |^3}\]

where m is the magnetic dipole moment, r is the displacement vector to where we are measuring the field, and n is a unit vector that points to where we are measuring.

To find the magnitude (which is what we really care about), we just take the dot product of the vector with itself and take the square root.  Working this out we get

\[ B\left(\vec{r}\right) = \frac{|\vec{m}|}{r^3}{\left[ 3\cos^2{\theta}+1\right]}^{1/2} \]

where theta is the angle between the magnetic moment vector and the direction vector n.  But we are just looking for a rough estimate here so let's just set the cosine term to one.  Now we have

\[ B\left(r\right) = \frac{2|\vec{m}|}{r^3}\]

We can now use the above to our advantage.  Since we are assuming we know the polar magnetic field strength, we can rearrange and solve for the magnetic moment.  At the pole of a star the distance is just going to be the radius, so for radius R and field strength Bp, we get

\[ |\vec{m}|} = \frac{1}{2}B_{p}R^3 \]

Plugging this back in, we get a nice little formula for the strength of the magnetic field in terms of the stellar radius and the polar field strength

\[B(r) = B_{p}{\left(\frac{R}{r}\right)}^3 \]

And we are almost there!  Rearranging now for r, we get

\[r = R{\left[\frac{B_p}{B(r)}\right]}^{1/3} \]

Huzzah!  Now we just need to plug in some values.  Well, we'll use Bp  = 10^15 gauss, B(r) = 1000 gauss (strong enough field to erase credit cards) and R = 10 km, which gives...

\[ r \approx 10km \times {\left(\frac{10^{15}gauss}{10^{3}gauss}\right)}^{1/3} \]

so

\[ r \approx \mbox{100,000 km} \]

The moon is about 380,000 km away.  So we find that the magnetar will erase all credit cards up to a little over a quarter the distance to the moon.  Not bad!  However, all this talk of "half" and "quarter" is a bit misleading given that our best guesses here will be order of magnitude.

But, overall, we see that a magnetar at roughly the Earth-Moon distance would have a good shot at erasing your credit cards.  Fun fact confirmed!

[1]  For a really nice Scientific American article about magnetars, see here.  For more information than you could probably ever want, see here.

[2]  For those of you who prefer your magnetic field strengths given in units named after someone played by David Bowie in a movie, you may note the conversion:  1 gauss = 10^-4 tesla.

28 comments:

  1. ...to say nothing of the effect of gravitation.

    ReplyDelete
    Replies
    1. Great Article Cyber Security Projects projects for cse Networking Security Projects JavaScript Training in Chennai JavaScript Training in Chennai The Angular Training covers a wide range of topics including Components, Angular Directives, Angular Services, Pipes, security fundamentals, Routing, and Angular programmability. The new Angular TRaining will lay the foundation you need to specialise in Single Page Application developer. Angular Training

      Delete
  2. This comment has been removed by the author.

    ReplyDelete
  3. Amazing post.Very useful to me.I liked it .Take a look to my blog cash against card at low interest.

    ReplyDelete
  4. Yes, you are absolutely correct.your blog is giving very useful knowledge for all, i'm sharing your information to all friends.
    Am providing
    Cash On Credit Card In Chennai
    at low interest.

    ReplyDelete
  5. Hi, I really like your blog you’ve written very well. I must say you have lot of knowledge about this but I want to suggest you something that if you are looking forb Free ad Posting Websites www.helpadya.com there is one more website www.helpadya.com

    ReplyDelete
  6. If you want your ex-girlfriend or ex-boyfriend to come crawling back to you on their knees (no matter why you broke up) you got to watch this video
    right away...

    (VIDEO) Have your ex CRAWLING back to you...?

    ReplyDelete
  7. Very well written and informative blog!! I am sure that who want to expand their knowledge about cards and want to be a credit cards will reap out benefits by reading this resource. Moving forward, if you want to gain more knowledge about credit cards, this link will help you. credit cards for bad credit

    ReplyDelete
  8. Every student has the chance of enjoying our affordable custom dissertation help. The writers hired at the company are legitimate paper writing services writers with significant experience.

    ReplyDelete
  9. Your search for Custom Research Paper Writing Services ends here. Welcome to the home of best essay writers who are qualified in diverse fields. Our
    Research Paper Writing Service
    is proof that we are right near you. It is easy, place your order and get original plagiarism free assignments. What’s more, we keep everything confidential.

    ReplyDelete
  10. Are you struggling with identifying an online Annotated Bibliography Services provider which is credible to undertake your task? Do not let tedious Custom Research Paper Services tasks sap you of energy unnecessarily, online Custom Research Paper Writing Service delivery comes with its own set of challenges.

    ReplyDelete
  11. Are you unsure about the confidentiality of Legitimate Custom Essay Writing Services? Is the deadline to submit your Professional Custom Essay fast approaching and are seeking Already Written Custom Essay that suits your precise requirements?

    ReplyDelete
  12. Our online assignment help is the most trusted among students from all universities across Australia. At MyAssignmentHelp, we suggest you relax more and concentrate on other important tasks and trust us to avail the best online assignments help.

    ReplyDelete
  13. "Best Assignment Experts" is currently one the best assignment helper across the globe. With years of experience, this site has been functioning in foreign countries too! It now provides its top services to countries like Australia, Canada, the USA, and entire Asia. With its aim to reach further student communities, we provide services at extremely affordable rates. Assignment Helper

    ReplyDelete
  14. Perdisco MYOB services have become extremely famous around the globe, especially for students opting for accounting and finance. At MyPerdiscoHelp.com, you can avail top quality Perdisco help at an affordable rate. Our MYOB Practice set is extremely low priced and affordable. Our experts are also student-friendly and approachable.

    ReplyDelete

  15. Assignment Help Canada

    Do you need assignment help Canada? If yes, come to the best assignment expert. Not just in Canada, we are offering quality academic assignment writing contents in Australia, UK, US, and UAE also. Get the Best Assignment Help Canada at an affordable price. Students across the globe have loved our services.

    ReplyDelete
  16. Myperdiscohelp.com assists accounting students at every step of Perdisco Login Our scholars and professionals are ready to assist and provide with the best, outstanding quality assignment help delivered on time. We are available 24/7 round the clock and provide cheapest and very affordable assignments. We guaranteed to an A+ grade in Perdisco.

    ReplyDelete

  17. Essay Writer Services

    Essay writer services by PhD. experts, Master's Degree graduates, and a writing specialist from Best assignment expert, we assure to secure good grades for students. We offer high-quality assignment and Essay Writer Services in the world.We are 24/7 available and provide a free Turnitin report.

    ReplyDelete
  18. If you are looking for Myob practice set solutions from any online Perdisco help delivery site, the best place to contact is Myperdiscohelp.com. We are a team of Perdisco experts who are immensely experienced, dedicated and knowledgeable. They are ready 24*7 to help you with your Perdisco assignments.

    ReplyDelete



  19. Canada Assignment Help

    Do you have lots of pending assignments to complete in Canada? The author further delays, avail our Canada Assignment Help services at Best assignment experts and give yourself some relief.

    ReplyDelete
  20. The academic overburden and pressure on students aren’t unknown to people. TRUSTED ONLINE Perdisco PRACTICE SET We very well know what students have to go through the constant pressure of semesters, examinations and assignment submissions. It becomes very difficult for students to submit their assignments on time and focus on their studies simultaneously. In this process, they end up submitting low-quality assignments to colleges.

    ReplyDelete
  21. My Assignment expert is the master of the entire assignment writing provider in Australia. It is one of the leading website since 2015.
    Management assignment help
    Dissertation proposal help

    ReplyDelete
  22. Don't forget another good way of simplifying your writing is using external resources (such as DigitalEssay.net ). This will definitely make your life more easier

    ReplyDelete
  23. Really nice and interesting post. I was looking for this kind of information and enjoyed reading this one. Keep posting. Thanks for sharing. when will kenpoly hnd admission form be out

    ReplyDelete
  24. Get Custom Assignment Help from Professionals. My Assignment Help, has a dedicated team of academic experts who are capable to provide the best advice for your assignment help, , who have many years of experience of practice.

    ReplyDelete