Question

A toroid has a core (nonferromagnetic) 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 : (a) Outside the toroid (b) Inside the core of the toroid (c) In the empty space surrounded by the toroid.

• A. (a)$2\times {10}^{-2}T$(b)$3\times {10}^{-2}T$(c)$3\times {10}^{-2}T$
• B. (a)$4\times {10}^{-2}T$(b)$3\times {10}^{-5}T$(c)$0\times {10}^{-2}T$
• C. (a)$0\times {10}^{-2}T$(b)$3\times {10}^{-2}T$(c)$0\times {10}^{-2}T$
• D. (a)$3\times {10}^{-2}T$(b)$3\times {10}^{-2}T$(c)$1\times {10}^{-2}T$

Answer 1

The correct option is C (a)$0\times {10}^{-2}T$

(b)$3\times {10}^{-2}T$

(c)$0\times {10}^{-2}T$

Given:r=25 cm ,R=26 cm, I=11 A, N=3500 A

Solution: This question is formula based .

(a) Outside the toroid:

Current flow outside the toroid is zero so magnetic field outside the toroid is zero

(b)Inside the toroid:

$B={\mu }_{0}ni$

Here $n=\frac{N}{2\pi l}$$=\frac{N}{2\pi \left(\frac{r+R}{2}\right)}$

After putting values ,we get that :n = $\frac{3500}{\pi \times 0.51}$

$B={\mu }_{0}i\times \frac{N}{2\pi l}$

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

B=0.03T

(c)In the empty space surrounded by the toroid:

Toroid is considered as a ring shaped closed toroid..Sp we can say that the toroid is endless cylinder. Magnetic field in the empty space surrounded by the toroid is zero

Hence the correct option is C