- #1
stunner5000pt
- 1,461
- 2
you are given a wire of length L and that carries a uniform current i through it.
the wire can bent into either a circle or a square
which shape gives the maximum magnetic field at its center?
for the circle
[tex] B = \frac{\mu_{0}}{4 \pi} \int \frac{i ds \cross r}{r^3} [/tex]
im not qutie sure about the s part since ds = L, riught? so ds is constant value... and so is R so we should get
[tex] B = \frac{\mu_{0} i}{4 \pi R^2} [/tex]
where [tex] R = \frac{L}{2 \pi} [/tex]
so [tex] B = \frac{\mu_{0} i \pi}{L^2} [/tex]
now for the squar
the problem is ds is a cosntant value, but r is not because it varies from s/2 to [itex] \frac{s}{\sqrt{2}} [/itex]
so what do i do? Can i use the square as an Amperian loop and solve it like so
[tex] B (s^2) = \mu_{0} i [/tex]
since 4S = L, s = L/4 so
[tex] B = \frac{16 \mu_{0} i}{L^2} [/tex]
thus the magnetic field at the center due to th square loop is greater becasue 4 > pi?
Also i am a bit confused as to when i use the Ampere's law and Biot Savart Law, can the Ampere's law be used for the above described situations or not?
Please help! Your advice is greatly appreciated!
the wire can bent into either a circle or a square
which shape gives the maximum magnetic field at its center?
for the circle
[tex] B = \frac{\mu_{0}}{4 \pi} \int \frac{i ds \cross r}{r^3} [/tex]
im not qutie sure about the s part since ds = L, riught? so ds is constant value... and so is R so we should get
[tex] B = \frac{\mu_{0} i}{4 \pi R^2} [/tex]
where [tex] R = \frac{L}{2 \pi} [/tex]
so [tex] B = \frac{\mu_{0} i \pi}{L^2} [/tex]
now for the squar
the problem is ds is a cosntant value, but r is not because it varies from s/2 to [itex] \frac{s}{\sqrt{2}} [/itex]
so what do i do? Can i use the square as an Amperian loop and solve it like so
[tex] B (s^2) = \mu_{0} i [/tex]
since 4S = L, s = L/4 so
[tex] B = \frac{16 \mu_{0} i}{L^2} [/tex]
thus the magnetic field at the center due to th square loop is greater becasue 4 > pi?
Also i am a bit confused as to when i use the Ampere's law and Biot Savart Law, can the Ampere's law be used for the above described situations or not?
Please help! Your advice is greatly appreciated!