Question

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

• A. $10.18\times {10}^{-2}V$
• B. $9.66\times {10}^{2}V$
• C. $10.18\times {10}^{-3}V$
• D. $1.51\times {10}^{-2}V$

Answer 1

The correct option is C $10.18\times {10}^{-3}V$

Change in magnetic field in $10s=2.0T$
As $ϵ=\frac{-d\varphi }{dt}=-A\frac{dB}{dt}(\because \varphi =BA)$
Circumference of patient's trunk,
$2\pi r=0.8m$(given)
$\therefore r=\frac{0.8}{2\pi }m=\frac{0.4}{\pi }m$
Area of cross section, $A=\pi r^2=\pi {\left(\frac{0.4}{\pi }\right)}^2=\frac{0.16}{\pi }{m}^2$
$\therefore |ϵ|=\frac{0.16}{\pi }\times \frac{2}{10}V\approx 10.18\times {10}^{-3}V$.