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Circular loop having radius r, carrying current J, produces magnetic field at the centre of the loop is B. What will be the magnetic dipole moment of this loop ?

Asked in GUJCET 2021 · Magnetic moment of loops and charges

• (1) (4π B r³)/(μ₀)
• (2) (2π B r³)/(μ₀)
• (3) (π B r³)/(μ₀)
• (4) (π B r³)/(4μ₀)

Step-by-step solution

Why the other options are wrong

• (1) Follows from B=(μ₀ J)/(4r), which is the field at the centre of a semicircular arc, not of a whole loop. A full loop gives (μ₀ J)/(2r) and so half this current.
• (3) Follows from B=(μ₀ J)/r, the 2 of the loop formula dropped. That halves the current recovered from B and so halves the moment.
• (4) One eighth of the right answer; no single slip in B=(μ₀ J)/(2r) or in m=Jπ r² produces it. Sanity check: J=(2rB)/(μ₀), so m=(2π Br³)/(μ₀).

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