Two short bar magnets of magnetic moments M and 2M have their centres on the same straight line, separated by distance d. Their magnetic moments are parallel to this line and point in the same direction. A neutral point lies between them. Its distance x from the magnet of moment M is:
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Question

Two short bar magnets of magnetic moments M and 2M have their centres on the same straight line, separated by distance d. Their magnetic moments are parallel to this line and point in the same direction. A neutral point lies between them. Its distance x from the magnet of moment M is:

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G1 Physics · Accepted Answer

Between the magnets, their axial fields are opposite. At the neutral point, (μ₀/4π)·2M/x³ = (μ₀/4π)·2(2M)/(d−x)³. Cancel common factors: 1/x³ = 2/(d−x)³. Thus, (d−x)/x = ∛2. So, d = x(1+∛2), and therefore, x = d/(1+∛2).