Question

1. Suppose that the dipole moment associated with an iron atom of an iron bar is 1.6 × 10^-23 J/T. Assume that all the atoms in the bar, which is 4.3 cm long and has a cross-sectional area of 1.5 cm², have their dipole moments aligned. (a) What is the dipole moment of the bar? (b) What torque must be exerted to hold this magnet perpendicular to an external field of 1.2 T? (The density of iron is 7.9 g/cm³ and its molar mass is 55.9 g/mol.)

2.Suppose that a parallel-plate capacitor has circular plates with radius R = 26 mm and a plate separation of 4.1 mm. Suppose also that a sinusoidal potential difference with a maximum value of 170 V and a frequency of 82 Hz is applied across the plates; that is,
V = (170 V) sin[2π(82 Hz)t].
Find B_max(R), the maximum value of the induced magnetic field that occurs at r = R.

Answer 1

O MFe = 1.681023 JT l=413cm A = 115 cm² , f = 7.9 g/cm² , M=55. 9 gimol (a) m e SV = Se A =(7.9) (4:3)(1.5) m= 50.955 g I No. of iron atoms (N) = NAM N = (6.023X1023) 50.955) - 55.9 N= 5.4898 1023 Dipole moment (M) = NU Fe = (5.489x10²²) 6. 6x10 23). Il a 808 Am² (b) Torque LT ) = B = (8.8) (112) T= 10.5 Nm

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