What is the magnetic field around a long, current-carrying wire?

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The magnetic field around a long, current-carrying wire can be determined using the Law of Biot-Savart, which states that the field at a distance r from the wire is given by the formula (μI/2πr). Inside the wire, the magnetic field varies depending on the current distribution, while outside the wire, it follows the aforementioned formula. To solve for the magnetic field, applying Gauss's law for magnetism is essential. The discussion highlights the need for a straightforward approach without complex equations. Understanding these principles is crucial for accurately calculating the magnetic field in different regions around the wire.
Master J
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A long, current carrying wire has a radius R and current I.
What is the magnetic field inside, and outside the wire?


Now, if it asked what is the field a distance r from the wire, I could simply use the Law of Biot & Savart (mu.I/2.pi.r). I havn't dome electricity in a while and I am stuck on this one.

I am sure its simple, I just need a nudge.

Thanks guys.
 
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I'm currently using my PDA so no complex equations.But you'll need to use the Gaussian surface for magnetic field.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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