Magnetic Induction at Point on Conductor: Biot-Savart Law

[ananthu]

Homework Statement

What is the magnetic induction at a point on a current carrying conductor itself according to biot -savart law? is it zero, infinity?

Homework Equations

The Attempt at a Solution

 

[Redbelly98]

Welcome to Physics Forums.

If you include the equation here, we can look at it and answer the question.

 

[ananthu]

Hello Redbelly, Thank you for your suggestion. Here I am giving the equation and elaborating my point. According to the Biot Savart law, the magnetic inducion due to a current element is given by dB = (μ_0 / 4π)(I dl sinθ / r^2). Applying this for an infinitely long straight conductor carrying current, we get the equation the magnetic induction at a point as B = μ_0 I /2πa where a is the perpendicular distance of the point from the conductor. My doubt is as follows: As the point approaches the conductor the value of a decreases and the B increases. This we can understand. But in a special case, when
a = o, ie. when the point lies on the conductor itself, according to the above equation B should become infinity. Does it make any sense?
In that case, can one tap infinite magnetic energy from the surface of a current carrying conductor? My common sense tells the value of B at a point on the conductor should be zero. But,it contradicts with the equation. I will be grateful to you if you have an explanation. Good wishes.

 

[Redbelly98]

Yes, for an infinitesimally thin conductor, B would be infinite on that conductor according to the Biot-Savart Law.

Since real conductors are not infinitesimally thin (i.e. the conductor's radius is not zero), B is not actually infinite. B will have some finite value at the surface, and be zero at the central axis of the conductor.

 

[ananthu]

Thank you for your reply. Again, I have slight confusion regarding your statement. How B could be zero, on the centrl axis of the conductor, where the value of 'a' ie, the distance of the said point is zero? It should be only infinity again? Will you please elaborate that particular point alone with a little more clarity?

 

[dx]

The formula

$$B = \frac{\mu_{0}I}{2 \pi r}$$

Works only for r > a, where a is the radius of the wire. If r < a, then the formula is

$$B = \frac{\mu_{0}I r}{2 \pi a^2}$$

(assuming a uniform current density)

which gives 0 when r = 0.

 

[ananthu]

Thank you all for your kind replies. Now I have a technical difficulty in using this Physics Forum site. Since I am new to this site I face some operational problems. How to post new questions on an entirely new topic? When I click " home work and classwork questions", I don't get page related to posting questions. Will anyone kindly help me as to how to proceed further for posting questions on different topics?

 

[Redbelly98]

From www.physicsforums.com, click on one of the subforums -- there is a long list of them there. For example, the Introductory Physics Homework subforum that this thread is posted in:

https://www.physicsforums.com/forumdisplay.php?f=153

Once you are in a subforum, you can start posting by clicking the "New Topic" button:

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EDIT:

When I click " home work and classwork questions", I don't get page related to posting questions.

You'll have to choose one of the subforums in "home work and coursework questions". For example, Introductory Physics, Advanced Physics, etc.

 

[ananthu]

Thank you. I got it. Kudos to the members of the physics forum (like you)for their concern and sincerety in helping the new members! In fact, I feel I had missed this wonderful forum all these years...