For MRI, a patient is slowly pushed in a time of 10 s within the coils of the magnet where magnetic field is B = 2.0 T. If the patient's trunk is 0.8 m in circumference, the induced emf around the patient's trunk is

10.18 x 10^-2 V

9.66 × 10² V

10.18 × 10^-3 V

1.51 × 10^-2 V

Solution

10.18 × 10^-3 V

Change in magnetic field in 10 s = 2.0 T

ε = $- \frac{dϕ}{dt}$

= $- A \frac{dB}{dt}$ ( $∵$ $ϕ$ = BA )

Circumference of patient's trunk

2 $π$ r = 0.8 m (given)

∴ r = $\frac{0.8}{2 π}$ m

r = $\frac{0.4}{π}$ m

Area of cross section

A = $π r^{2}$

A = $π {(\frac{0.4}{π})}^{2}$

A = $\frac{0.16}{π}$ m²

∴ $|ε| = \frac{0.16}{π} \times \frac{2}{10}$ V

$|ε|$ ≈ 10.18 × 10^-3 V

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