fluidistic
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1. The problem statement, all variables and given/known data
See the picture for a clear description of the situation. I must find the magnetic field at point [tex]P_1[/tex] and [tex]P_2[/tex]. The picture represent a transversal cut of a wire carrying a current I going off the page to our direction. The density of the current is J.
2. Relevant equations None given.
3. The attempt at a solution
I used Ampere's law. I know the figure doesn't seem enough symmetric to use Ampere's law, but I think it is. I'll explain why: I though the problem like if there were 2 wires. One of radius 2a and with a current I in our direction and another wire with radius a with current I/4 (since the area of the "hole" of the wire is one fourth of the area of what would be a circular wire of radius 2a.)
Thanks to Ampere's law, [tex]B_1=\frac{\mu _0 I}{2 \pi d}[/tex].
[tex]B_1(P_1)=\frac{\mu _0 I}{2 \pi (2a+d)}[/tex] and [tex]B_1 (P_2)= \frac{\mu _0 I}{2 \pi (2a+d)}[/tex].
Now [tex]B_2 =\frac{\mu _0 I}{8\pi d'}[/tex].
[tex]B_2(P_1)=\frac{\mu _0 I}{8\pi (a+d)}[/tex] and [tex]B_2(P_2)=\frac{\mu _0 I}{8 \pi (3a+d)}[/tex].
At last, [tex]B(P_1)=B_1(P_1)+B_2(P_1)[/tex] and [tex]B(P_2)=B_1(P_2)+B_2(P_2)[/tex].
Am I right?
See the picture for a clear description of the situation. I must find the magnetic field at point [tex]P_1[/tex] and [tex]P_2[/tex]. The picture represent a transversal cut of a wire carrying a current I going off the page to our direction. The density of the current is J.
2. Relevant equations None given.
3. The attempt at a solution
I used Ampere's law. I know the figure doesn't seem enough symmetric to use Ampere's law, but I think it is. I'll explain why: I though the problem like if there were 2 wires. One of radius 2a and with a current I in our direction and another wire with radius a with current I/4 (since the area of the "hole" of the wire is one fourth of the area of what would be a circular wire of radius 2a.)
Thanks to Ampere's law, [tex]B_1=\frac{\mu _0 I}{2 \pi d}[/tex].
[tex]B_1(P_1)=\frac{\mu _0 I}{2 \pi (2a+d)}[/tex] and [tex]B_1 (P_2)= \frac{\mu _0 I}{2 \pi (2a+d)}[/tex].
Now [tex]B_2 =\frac{\mu _0 I}{8\pi d'}[/tex].
[tex]B_2(P_1)=\frac{\mu _0 I}{8\pi (a+d)}[/tex] and [tex]B_2(P_2)=\frac{\mu _0 I}{8 \pi (3a+d)}[/tex].
At last, [tex]B(P_1)=B_1(P_1)+B_2(P_1)[/tex] and [tex]B(P_2)=B_1(P_2)+B_2(P_2)[/tex].
Am I right?
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