Question

A body enters an MRI machine in 10 sec. If the magnetic field is 1.5 T and circumference of the MRI machine is 0.9 m then find out emf induced in the body.
A. 0.96 V
B. 9.6 V
C. 9.6 mV
D. 96 mV

Answer 1

Hint – Get the radius with the help of circumference then calculate the area and then get the change in flux since change in flux with respect to time is the emf induced.
Formula used - $\phi = BA$, $emf = \dfrac{{\Delta \phi }}{{\Delta t}}$.

Complete Step-by-Step solution:
The circumference of the circle given is 0.9m.
Let the radius be r then the circumference can be equated with the formula as:
$
  2\pi r = 0.9 \\
  r = \dfrac{{0.9}}{{2\pi }} \\
$
Therefore area of the circular magnetic field is $\pi {r^2} = \dfrac{{\pi {{(0.9)}^2}}}{{{\pi ^2}{2^2}}} = \dfrac{{0.81}}{{4\pi }} = 0.064{m^2}$
We know that flux $\phi {\text{ = BA = magnetic}}\,{\text{field}}\,{\text{x}}\,{\text{Area}}$
Initial flux $\phi = 0$ (when the body did not entered)
Final flux = $\phi = BA = 1.5{\text{ x 0}}{\text{.064 = 0}}{\text{.096 weber}}$
Therefore the change in flux is $\Delta \phi = 0.096 - 0 = 0.096$ weber
The emf induced = $\dfrac{{\Delta \phi }}{{\Delta t}} = \dfrac{{0.096\,weber}}{{10s}} = 0.0096\,$volt or 9.6 mV.
The right option is C.

Note – To solve this problem you need to know the formulas of flux and emf induced $\phi = BA$, $emf = \dfrac{{\Delta \phi }}{{\Delta t}}$. The induced emf always tries to stop the change therefore its direction is opposite to the supplied emf and it generates the magnetic field such that the change is stopped.