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Two circular coils are concentric, each having a radius of 2π cm, and the planes of the coils are mutually perpendicular. If currents of 3 A and 4 A flow through the two coils, respectively, what is the magnitude of the magnetic induction at the common centre? Take μ0 = 4π × 10⁻⁷ Wb/A·m.

1. 10⁻⁵
2. 12 × 10⁻⁵
3. 7 × 10⁻⁵
4. 5 × 10⁻⁵

Correct answer: 5 × 10⁻⁵

Solution

The magnetic induction at the center of two perpendicular coils can be calculated using the formula for the magnetic field due to a circular coil, which is proportional to the current and inversely proportional to the radius. By applying the formula for both coils and considering their perpendicular arrangement, the resultant magnetic induction is found to be 5 × 10⁻⁵ Wb/m².

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