6. A toroid has a core of inner radius 20 cm and outer
radius 22 cm around which 4200 turns of a wire are
wound. If the current in the wire is 10 A, what is the
magnetic field (i) inside the core of toroid (ii) outside
the toroid and (iii) in the empty space surrounded
by the toroid. [Ans. (i) 0.04 T (ii) Zero (iii) Zero]
Plz Give answer with full explanation
Answers
Answer:
Explanation:
Here, inner radius, r1=20cm.
Outer radius, r2=22cm, I=10A
∴ Mean radius of toroid,
r=r1+r22=20+222=21cm=0⋅21m
Total length of toroid=circumference of toroid
=2πr=2π×0⋅21
=0⋅42πm
Total number of turns, N=4200
∴ Number of turns per unit length will be,
n=42000⋅42π=10000πm−1
(a) Magnetic field induction inside the core of
toroid, B=μ0nI=4π×10−7x10000π×10=0⋅04T
(b) Magnetic field induction outside the toroid is zero, since the field is only confined inside the core of the toroid on which winding has been made.
(c) Magnetic field induction in the empty space surrounded by toroid is also zero.
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Given:
A toroid has a core of inner radius 20 cm and outer
radius 22 cm around which 4200 turns of a wire are
wound.
the current in the wire is 10 A
Find:
If the current in the wire is 10 A, what is the
magnetic field
(i) inside the core of the toroid
(ii) outside the toroid and
(iii) in the empty space surrounded by the toroid.
Solution:
Here,
inner radius,
r1=20cm.
Outer radius,
r2=22cm,
I=10A
∴ Mean radius of toroid,
r = r1+r2/2 = 20+22/2=21cm = 0⋅21m
Total length of toroid=circumference of toroid
= 2πr = 2π × 0⋅21
= 0⋅42πm
Total number of turns, N = 4200
∴ Number of turns per unit length will be,
n = 4200/0⋅42π = 10000/π m−1
(a) Magnetic field induction inside the core of
toroid, B = μ0nI = 4π×10−7x10000π×10 = 0⋅04T
(b) Magnetic field induction outside the toroid is zero since the field is only confined inside the core of the toroid on which winding has been made.
(c) Magnetic field induction in the empty space surrounded by toroid is also zero.