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# A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound. If the current in the wire is 11 A, what is the magnetic field inside the core of the toroid.

17.(b) A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound. If the current in the wire is 11 A, what is the magnetic field inside the core of the toroid?

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The magnetic field inside the core of a toroid is given by

$B=\frac{\mu _{o}NI}{l}$

Total number of turns(N)=3500

Current flowing in toroid =11 A

Length of the toroid, l=

$\\l=2\pi \left (\frac{ r_{1}+r_{2}}{2} \right )\\ \\l=\pi ( r_{1}+r_{2})\\ \\l=\pi (0.25+0.26)\\ \\l=0.51\pi$ (r1=inner radius=25 cm, r2=outer radius=26 cm)

$B=\frac{4\pi \times 10^{-7}\times 3500\times 11}{0.51\pi }=0.031 T$

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