Question

Calculate the magnetic fields (B_o) that correspond to proton resonance frequencies of 60MHz and 30MHz in gauss and Tesla units

Answer 1

As we know,

\(\mu=({\frac{γ}{2\pi}})Bo\)

where,

\(\mu\) = frequency

γ = g y ro magnetic ratio

B_o = magnetic field

as we know (γ/2π) for proton = 42.578 MH_z.T^-1

\(∴ \frac{for\,frequency\,60\,MH_z}{60\times10^6}\) = (42.578 x 10⁶ s^-1.T^-1)x Bo

\(Bo=(\frac{60}{42.578})T=1.40917\) Tesla or B_o = 1.41 Tesla

or B_o = 14092.gauss (1 Tesla = 10000 gauss)

for frequency = 300 MHZ

300 x 10⁶ s^-1 = (42.578 x 10⁶ s^-1 T^-1) x Bo

\(Bo = (\frac{300}{42.578})Tesla\)

B_o = 7.04589 Tesla

or B_o = 70459 gauss (∵ 1 Tesla = 10000 gauss)