Suppose for the nucleus of interest, the gyromagnetic ratio is ƒ× = 2.675x108 T-1 s-1 (radians is an implicit unit here) or ƒ×ƒ}ƒ¢ƒà = 42.58 MHz/T. If the applied magnetic field is 3T, determine the resonant frequency of the spins (in MHz or radian/s).

Assume we have two objects located at x = 0 and x = 10 cm and we apply a magnetic field variation (gradient) in the x direction of 3x10-5 T/cm. Determine the frequency difference between the objects

γ= 2.675•10⁸ T⁻¹•s⁻¹

γ/2π =42.58 MHz/T
f= γ•B = 2.675•10⁸•3 = 8.0250•10⁸s⁻¹
B1=3 + 3•10 ⁻⁵•10=3+3•10⁻⁴ T=3.0003 T
f1= γ•B1 = 2.675•10⁸•3.0003 = 8.0258•10⁸ s⁻¹
Δf=f1-f=8.0258•10⁸-8.0250•10⁸=8•10⁴= 80000 s⁻¹