Question

Using a magnet with a moment of inertia 2.1×10⁻⁴ kg⋅m², you acquire the following data: L=12 cm, D=23 cm, and T=5.0 s. Calculate (a) the value for Z (in SI units) and (b) the value for the horizontal component of the Earth's magnetic field (in μT ).

Answer 1

The value for Z is 3.01×10⁻⁵ T and the value for the horizontal component of the Earth's magnetic field is 6.67×10⁻⁵ C.

Step-by-step explanation:

To calculate the value for Z (in SI units), we can use the formula T = 2π√(I/Z). Rearranging the formula, we find that Z = (4π²I)/T². Plugging in the given values, we get Z = (4π² * 2.1×10⁻⁴ kg⋅m²)/(5.0 s)² = 3.01×10⁻⁵ T.

To calculate the value for the horizontal component of the Earth's magnetic field, we can use the formula B = μ₀I/2πR. Rearranging the formula, we find that I = (2πB * R)/μ₀. Plugging in the given values and using the value for μ₀, we get I = (2π * 5.0×10⁻⁵ T * 0.12 m)/(4π×10⁻⁷ T⋅m/A) = 6.67×10⁻⁵ C.

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