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Consider an ideal toroid of average radius 16.0 cm with 240 turns. A current of 10 A is maintained in it. The magnitude of magnetic field inside the t
Question

Consider an ideal toroid of average radius 16.0 cm with 240 turns. A current of 10 A is maintained in it. The magnitude of magnetic field inside the toroid is [(μ04π)=107(\frac{μ_0}{4π})=10^{-7}​ Tm/A]:

A.

6.0 mT

B.

9.0 mT

C.

3.0 mT

D.

1.5 mT

Correct option is C

We are given:The radius of the toroid r=16.0 cm=0.16 mNumber of turns N=240Current I=10 AThe magnetic constant μ04π=107 Tm/AThe formula for the magnetic field inside a toroid is:B=μ0NI2πr\text{We are given:} \\\text{The radius of the toroid } r = 16.0 \, \text{cm} = 0.16 \, \text{m} \\\text{Number of turns } N = 240 \\\text{Current } I = 10 \, \text{A} \\\text{The magnetic constant } \frac{\mu_0}{4\pi} = 10^{-7} \, \text{Tm/A} \\\text{The formula for the magnetic field inside a toroid is:} \\B = \frac{\mu_0 N I}{2\pi r}

 B=2×107×240×100.16=3×103 T=3.0 mT\ B = \frac{2 \times 10^{-7} \times 240 \times 10}{0.16} \\= 3 \times 10^{-3} \, \text{T} = 3.0 \, \text{mT}​​​

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