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Magnetic dipole and its field (axial and equatorial)

Magnetism and matter · Physics

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Problem: Calculate the magnetic field at a point on the axial line and the equatorial line of a bar magnet with a magnetic moment M = 2.5 A m^2 at a distance r = 0.1 m from its center. Use mu_0 / 4 pi = 10^-7 T m / A. Step 1: Identify the formula for the axial field. B_axial = (mu_0 / 4 pi) * (2M / r^3). Step 2: Substitute the values for the axial field. B_axial = 10^-7 * (2 * 2.5 / (0.1)^3). Step 3: Calculate the denominator. (0.1)^3 = 0.001. Step 4: Calculate the fraction. (2 * 2.5) / 0.001 = 5 / 0.001 = 5000. Step 5: Multiply by the constant. B_axial = 10^-7 * 5000 = 5 * 10^-4 T. Step 6: Identify the formula for the equatorial field. B_equatorial = (mu_0 / 4 pi) * (M / r^3). Step 7: Substitute the values for the equatorial field. B_equatorial = 10^-7 * (2.5 / 0.001). Step 8: Calculate the fraction. 2.5 / 0.001 = 2500. Step 9: Multiply by the constant. B_equatorial = 10^-7 * 2500 = 2.5 * 10^-4 T. Conclusion: The axial field is 5 * 10^-4 T and the equatorial field is 2.5 * 10^-4 T.

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