RRB Technician Grade 1 Model Paper 1

Concept:A neutral point is a point where the magnetic field of a bar magnet exactly cancels the horizontal component of Earth's magnetic field, giving zero net field.When the north pole of the magnet points towards the geographic south of Earth, the neutral points lie on the axial line of the magnet.For a point on the axial line, the magnetic field is given by $B = \frac{\mu_{0}}{4\pi}\frac{2M}{r^{3}}$.Explanation:Given: magnetic dipole moment, $M = 0.96\ \mathrm{Am}^{2}$.Horizontal component of Earth's magnetic field, $B_{H} = 24\ \mu\mathrm{T} = 24 \times 10^{-6}\ \mathrm{T}$.At the neutral point, the magnet's field equals $B_{H}$:$$\frac{\mu_{0}}{4\pi}\frac{2M}{r^{3}} = B_{H}$$Substituting the values:$$\frac{4\pi \times 10^{-7}}{4\pi} \times \frac{2 \times 0.96}{r^{3}} = 24 \times 10^{-6}$$$$\frac{1.92 \times 10^{-7}}{r^{3}} = 24 \times 10^{-6}$$$$r^{3} = \frac{1.92 \times 10^{-7}}{24 \times 10^{-6}} = 8 \times 10^{-3}$$$$r = \sqrt[3]{8 \times 10^{-3}} = 0.2\ \mathrm{m}$$Therefore, the neutral point is at $0.2\ \mathrm{m}$ from the center of the magnet, along the axis on either side of the poles.Answer:Option B: $0.2\ \mathrm{m}$ from the center of the magnet, along the axis.