The earth's magnetic field lines resemble that of a dipole at the centre of the earth. If the magnetic moment of this dipole is close to 8 × 10²² Am ², the value of earth's magnetic field near the equator is close to (radius of the earth = 6.4 × 10⁶ m) (a) 0.6 Gauss (b) 1.2 Gauss (c) 1.8 Gauss (d) 0.32 Gauss

Answer: (d). Beq = (μ₀)/(4π)M/R³ B = 10⁻⁷ × 8 × 10²²(6.4 × 10⁶)³ = 8 × 10¹⁵2.62 × 10²⁰ ≈ 3.05 × 10⁻⁵ T 1 G = 10⁻⁴ T ⇒ B ≈ 0.3 G So the answer is (d) 0.32 Gauss.

The earth's magnetic field lines resemble that of a dipole at the… | JEE Main 2013 (25 Apr, Shift 1)

Q14JEE Main 2013 · 25 APR · SHIFT 1Medium

Earth's Magnetism

The earth's magnetic field lines resemble that of a dipole at the centre of the earth. If the magnetic moment of this dipole is close to $8 \times 10^{22}$ Am $^{2}$ , the value of earth's magnetic field near the equator is close to (radius of the earth = $6.4 \times 10^{6}$ m)

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Answer: (d)

$B_{eq} = \frac{\mu_0}{4\pi}\frac{M}{R^3}$
$B = 10^{-7} \times \frac{8 \times 10^{22}}{(6.4 \times 10^6)^3} = \frac{8 \times 10^{15}}{2.62 \times 10^{20}} \approx 3.05 \times 10^{-5}\ \text{T}$
$1\ \text{G} = 10^{-4}\ \text{T} \Rightarrow B \approx 0.3\ \text{G}$
So the answer is (d) 0.32 Gauss.

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