Question

For MRI, a patient is slowly pushed in a time of 10s within the coils of the magnet where the 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$102V
C) 10.18$\times$ 10-3 V
D) 1.5$\times$10-2V

Answer 1

The question is asking about the induced EMF and the concept of induced EMF is given by Faraday’s Law:
$E = - \dfrac{{d\phi }}{{dt}}$ (Where $\phi$ is the flux induced, E is the EMF, t is the time)
Minus sign in the above equation comes from the Lenz law.
Using the above two laws we will conclude the problem.

Complete step by step solution:
Faraday’s law states that: Any change in the magnetic environment of the coil of conductors will cause a voltage (EMF) to be induced in the coil.
$E = - \dfrac{{d\phi }}{{dt}}$
Generally the change in flux takes place or we can say that the rate of change of flux causes induced EMF.
Electric Flux: electric flux is the property of an electric field that may be thought of as the number of electric lines of force that intersect at a given point.
Let’s calculate the EMF induced:
We have: $E = - \dfrac{{d\phi }}{{dt}}$
We can write $\phi$ = BA ( B is the magnetic field and A is the area).
$\therefore E = - A\dfrac{{dB}}{{dt}}$................1
B = 2Tesla and the circumference of the trunk is given 0.8m.
To calculate the area we must have the radius of the trunk.
Circumference is:
$\Rightarrow 2\pi r = 0.8 \\\ \Rightarrow r = \dfrac{{0.8}}{{2\pi }} = 0.127m \\\$
Radius of the circumference is 0.127m
Now area of the trunk:
$\Rightarrow \pi {r^2} = \pi {\left( {0.127} \right)^2}$
$\Rightarrow \pi {r^2} = \pi {\left( {0.127} \right)^2} =. 0509{m^2}$
We substitute all the values in equation 1
$\Rightarrow E = -. 0509 \times \dfrac{2}{{10}} \\\ \Rightarrow E =. 1019 \times {10^{ - 1}} \\\$
$\Rightarrow E = 10.19 \times {10^{ - 3}}$ (Multiply the numerator and denominator by 100)

Option 3 is correct.

Note: Lenz law which we have mentioned above states that the direction of the electric current which is induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field.