Chapter 28, Problem 054 A magnetic dipole with a dipole moment of magnitude 0.01

Question

Chapter 28, Problem 054 A magnetic dipole with a dipole moment of magnitude 0.0190 ? T s released rom rest in a uniform magnetic fied of magnitude 557 mT. The rotation of the di ed et magnetic force on it is unimpeded. When the dipole rotates through the orientation where its dipole moment is aligned with the magnetic field, its kinetic energy is 0.751 mJ. (a) What is the initial angle between the dipole moment and the magnetic field? (b) What is the angle when the dipole is next (momentarily) at rest? (a) Number Units b) Number Units

Explanation / Answer

Given,

u = 0.0190 J/T ; B = 55.7 mT ; E = 0.751 mJ

a)we can write from conservation of energy

K = U2 - U1

K = u B2 - (-u B1) = -u B cos(theta) + u B cos0

K = u B(1 - cos(theta))

1 - cos(theta) = K/u B

cos(theta) = 1 - K/u B

cos(theta) = (1 - 0.751 x 10^-3/(0.0190 x 55.7 x 10^-3) = 0.2904

theta = cos^-1(0.2904) = 73.12 deg

Hence, theta = 73.12 deg

b)The angle will remain same since there will be no dissipation of energy now.

theta = 73.12

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