Posting for the third time. High precision calculation is needed in order to get the answer, keeping the required asked units in mind. The whole question is a part of a single question and related to one another. This is one question divided into parts A, B, C, D, E, F, and G. MENTIONING AGAIN, HIGH PRECISION CALCULATION IS NEEDED, KEEPING THE UNITS IN ACCOUNT. Thank you.
A planet with Earth-like magnetic field can have such a bar magnet. We will treat it as a magnetic dipole. Its dipole moment is given by μ = m√(4π/3), where m is the magnetic moment. The dipole moment remains unchanged without the application of an external magnetic field. Suppose a uniform magnetic field is given by B = (40.03 + (35.0 * 10^7)e^(-a)), where a is the distance from the center of the bar magnet. When this magnetic field is applied, the bar magnet starts to rotate. At some instant during rotation, the torque is τ = (2055.2023883969796) * 10^2 N*m and the potential energy is U = 2890.651854292964 * 10^1 J. Find the x and y components of the magnetic dipole moment at this position.
y component of the dipole moment: -6.639226824 * 10^21 N*m/T
x component of the dipole moment: -6.713174996 * 10^20 N*m/T
Angle between magnetic dipole moment and magnetic field: 54.58785926 degrees
Find the x and y components of the magnetic dipole moment at the minimum potential energy position.
x component of the dipole moment: 3.530845564 * 10^3 N*m/T
y component of the dipole moment: 0
What is the magnitude of the magnetic dipole moment before it starts to rotate and at position 1?
Magnitude of magnetic dipole moment before rotation: N*m/T
Magnitude of magnetic dipole moment at position 1: N*m/T
How much external energy is required to keep the dipole in the maximum potential energy position?
Absolute value of external energy: 2890.651854292964 * 10^21 J
