A uniformly wound air-core toroid has 750 loops on it. The radius of the circle trough the center of its windings is 5 cm. What current in the winding will produce a field of 1.8 mT on this central circle?
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Given:
A uniformly wound air-core toroid has 750 loops on it. The radius of the circle trough the center of its windings is 5 cm.
To find:
What current in the winding will produce a field of 1.8 mT on this central circle?
Solution:
From given, we have,
The number of loops = N = 750 loops
The radius of the circle = r = 5 cm = 0.05 m
The magnetic field = B = 1.8 m T
We use the formula,
B = μ₀NI/2r
1.8 × 10^{-3} = (4π × 10^{-7} × 750 × I) / (2 × 0.05)
1.8 × 10^{-3} = 9.4247 × 10^{-7}I / 0.1
I = 1.8 × 10^{-3} × 0.1 / 9.4247 × 10^{-7}
I = 0.19 A
∴ The current in the winding will produce a field of 1.8 mT on this central circle is 0.19 A
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