Timeline for Magnetic field in a cylinder with an off-axis hole
Current License: CC BY-SA 3.0
10 events
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| Feb 25, 2014 at 10:57 | comment | added | Tobias | In general you also have to regard the direction of the field vectors and apply vectorial summation. But, in your special case this is rather simple since one of the fields is zero. It would be a nice excersice to calculate the field also in an off-axis point. | |
| Feb 25, 2014 at 9:24 | comment | added | user1887919 | $d>b$ so we don't need to worry about outer fields.I am confused as to the next step. We want the magnetic field at the centre of the cylinder. This is a superposition of a full cylinder and a smaller cylinder of opposite current density. So the net field at the centre of the cylinder is just the sum of these? | |
| Feb 24, 2014 at 21:28 | comment | added | Tobias | On the axis the field is zero because of continuity of $B$. This is all for the single circular cylindrical conductor. Now, you can combine the fields of two such things. Be careful, the field of the hole may be an outer field if $d<b$. | |
| Feb 24, 2014 at 20:48 | comment | added | user1887919 | So on the axis at $\rho=0$ the path length and magnetic field are both zero? | |
| Feb 24, 2014 at 18:47 | comment | added | Tobias | Yes, so we get $\vec{B}=\frac{1}{2}\mu_0 J\rho\,\vec{e}_\alpha$ inside the single conductor. Only at the boundary you get $\vec{B}=\frac{1}{2}\mu_0 J a\,\vec{e}_\alpha$. Ah yes, and what is the value at $\rho=0$ for a single conductor (i.e. on the axis)? | |
| Feb 24, 2014 at 18:41 | comment | added | user1887919 | Current enclosed is given by the product of the current density and the area so $I_{enc} = JA=J\pi \rho^2 $ Path length is just given by $2\pi\rho $? So then apply Ampere's law? | |
| Feb 24, 2014 at 18:04 | history | edited | Tobias | CC BY-SA 3.0 |
added 177 characters in body
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| Feb 24, 2014 at 17:59 | comment | added | Tobias | No, the field inside of the main cylinder is not constant. Consider a circular path around the axis with radius $\rho<a$. How large is the current enclosed by this path? How long is the path? This gives you the value of $H$ and $B$. | |
| Feb 24, 2014 at 16:32 | comment | added | user1887919 | This is what I had attempted before.I have calculated the magnetic field in the hole as stated in the question, but am confused about the field in the main cylinder. Is the field in the main cylinder (without a hole) given by $ \mu_0 Ja / 2$? | |
| Feb 24, 2014 at 13:40 | history | answered | Tobias | CC BY-SA 3.0 |