Two short bar magnets (length 1 cm each) have magnetic moments $1.20\ \text{A\,m}^2$ and $1.00\ \text{A\,m}^2$. They are placed on a table parallel to each other with N-poles pointing South, sharing a common magnetic equator, separated by $20.0\ \text{cm}$. The resultant horizontal magnetic induction at midpoint O is close to:
(Earth's horizontal component $B_H = 3.6 \times 10^{-5}\ \text{Wb/m}^2$)
At the midpoint O (on the equatorial line of both magnets), $r = 0.10\ \text{m}$:
Field due to each magnet on equatorial line: $B = \frac{\mu_0}{4\pi}\frac{M}{r^3}$
$B_1 = \frac{10^{-7} \times 1.20}{(0.10)^3} = 1.20\times10^{-4}\ \text{T}$
$B_2 = \frac{10^{-7} \times 1.00}{(0.10)^3} = 1.00\times10^{-4}\ \text{T}$
Both fields point in the same direction (both N-poles south, equatorial fields add).
Total from magnets $= 2.20\times10^{-4}\ \text{T}$. Adding Earth's component: $2.20 + 0.36 = 2.56\times10^{-4}\ \text{Wb/m}^2$.
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