A toroid has a core (non-ferromagnetic material) of inner radius 25 cm and outer radius 26 cm around which 3500 turns of 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?

Solution

Given,
Inner radius of torroid core, r₁ = 0.25 m
Outer radius, r₂ = 0.26 m
Number of turns, N = 3500
Current in the wire, I = 11 A

(i)    The magnetic field is zero outside the toroid because, there is no current flowing on outside of the torroid.

(ii) Magnetic field inside the core of the toroid,
$B = μ_{0} nI$    $B = \frac{μ_{0} NI}{l} (∵ n = \frac{N}{l} \to Number of turns per unit length)$

$I = 2 π (\frac{r_{1} + r_{2}}{2})$
$= π (r_{1} + r_{2}) = π (0.25 + 0.26) = π \times 0.51 m$

Putting the values
$B = \frac{(4 \times 10^{- 7}) \times 3500 \times 11}{π \times 0.51} = 3.02 \times 10^{- 2} T$

(iii) The magnetic field is zero in the empty space surrounded by the toroid also.

Some More Questions From Moving Charges And Magnetism Chapter

Two moving coil meters, M₁ and M₂ have the following particulars:
R₁ = 10 Ω N₁ = 30,
A₁ = 3.6 x 10^–3 m², B₁ = 0.25 T
R₂ = 14 Ω; N₂ = 42,
A₂ = 1.8 x 10^–3 m², B₂ = 0.50 T
(The spring constants k are identical for the two meters).
Determine the ratio of (a) current sensitivity and (b) voltage sensitivity of M₂ and M_1.

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