A device called a toroid (figure) is often used to create an almost uniform magetic fiedl in some enclosed area. The device consists of a conducting wire wraped around a ring (a torus) made of a non conducting material. For a toroid having `N` closely spaced turns of wire, calculate the magnetic field in the region occupied by the torus, a distasnce `r` from the centre.
A device called a toroid (figure) is often used to create an almost uniform magetic fiedl in some enclosed area. The device consists of a conducting wire wraped around a ring (a torus) made of a non conducting material. For a toroid having `N` closely spaced turns of wire, calculate the magnetic field in the region occupied by the torus, a distasnce `r` from the centre.
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To calculate this field we must evaluate `ointB.dI` over the circle of radius `r`. By symmetry we see that the magnitude of the field is constant on this circle and tangent to it.
so, `oint B.dI=Bl=B(2pir)`
Furthermore, the circular closed path surrounds `N` loops of wire each of which carries a current `i` . Therefore, right side of Eq. i is `mu_0 Ni` in this case
`:. oint B.dI=mu_0i_("net")`
or `B(2pir)=mu_0Ni`
or `B=(mu_0Ni)/(2pir)`
this result shows that `Bprop1/r`
and hence is non uniform in the region occupied by torus. However, if `r` is very large compared with the cross sectional radius of the torus, then the field is approximately uniform inside the torus.In that case
`N/(2pir)=n="number of turns per unit length of torus"`
`:. B=mu_0ni`
so, `oint B.dI=Bl=B(2pir)`
Furthermore, the circular closed path surrounds `N` loops of wire each of which carries a current `i` . Therefore, right side of Eq. i is `mu_0 Ni` in this case
`:. oint B.dI=mu_0i_("net")`
or `B(2pir)=mu_0Ni`
or `B=(mu_0Ni)/(2pir)`
this result shows that `Bprop1/r`
and hence is non uniform in the region occupied by torus. However, if `r` is very large compared with the cross sectional radius of the torus, then the field is approximately uniform inside the torus.In that case
`N/(2pir)=n="number of turns per unit length of torus"`
`:. B=mu_0ni`
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