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Two short bar magnets of length 1 cm each have magnetic moments 1.20 A m² and 1.00 A m² respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance 20.0 cm. The value of the resultant horizontal magnetic induction at the mid-point O of the line joining their centres is close to. (Horizontal component of earth's magnetic induction is 3.6 × 10⁻⁵ Wb/m²)

1. 3.6 × 10⁻⁵ Wb/m²
2. 2.56 × 10⁻⁴ Wb/m²
3. 3.50 × 10⁻⁴ Wb/m²
4. 5.80 × 10⁻⁴ Wb/m²

Correct answer: 2.56 × 10⁻⁴ Wb/m²

Solution

At the common equatorial mid-point each magnet gives B = (mu0/4pi)*m/r^3 with r=0.10 m: 1.2e-4 and 1.0e-4 Wb/m^2, both directed the same way (N->S), summing to 2.2e-4. Adding earth's horizontal component 0.36e-4 gives about 2.56e-4 Wb/m^2.

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