A toroidal solenoid with an air core has an average radius of 0.15 m, area of cross-section 12 x 10^–4 m² and 1200 turns. Obtain the self-inductance of the toroid. Ignore field variation across the cross-section of the toroid.

Solution

(a) Given, a toroidal solenoid.
Average radius, r = 0.15 m
Area of cross-section, A = 12 x 10^–4 m²Number of turns in the coil, n = 1200
Magnetic field is given by,

$B = μ_{0} n_{1} I = \frac{μ_{0} N_{1} I}{l} = \frac{μ_{0} N_{1} I}{2 πr}$

Total magnetic flux, $ϕ_{B} = N_{1} BA = \frac{μ_{0} N_{1}^{2} IA}{2 πr}$

But, $ϕ_{B} = LI$
$∴$ $L = \frac{μ_{0} N_{1}^{2} A}{2 πr}$

$L = \frac{4 π \times 10^{- 7} \times 1200 \times 1200 \times 12 \times 10^{- 4}}{2 π \times 0.15} H$
$= 2.3 \times 10^{- 3} H = 2.3 mH$

(b) Emf induced,

|E| = \frac{d}{dt} (ϕ_{2}),

where, Φ₂ is the total magnetic flux linked with the second coil.

Thus,

|E| = \frac{d}{dt} (N_{2} BA) = \frac{d}{dt} [N_{2} \frac{μ_{0} N_{1} I}{2 πr} A]

|E| = \frac{μ_{0} N_{1} N_{2} A}{2 πr} \frac{dI}{dt}

|E| = \frac{4 π \times 10^{- 7} \times 1200 \times 300 \times 12 \times 10^{- 4} \times 2}{2 π \times 0.15 \times 0.05} V

= 0.023 V

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Electric Charges And Fields

A toroidal solenoid with an air core has an average radius of 0.15 m, area of cross-section 12 x 10^–4 m² and 1200 turns. Obtain the self-inductance of the toroid. Ignore field variation across the cross-section of the toroid.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

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Electric Charges And Fields

A toroidal solenoid with an air core has an average radius of 0.15 m, area of cross-section 12 x 10–4 m2 and 1200 turns. Obtain the self-inductance of the toroid. Ignore field variation across the cross-section of the toroid.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A toroidal solenoid with an air core has an average radius of 0.15 m, area of cross-section 12 x 10^–4 m² and 1200 turns. Obtain the self-inductance of the toroid. Ignore field variation across the cross-section of the toroid.

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?