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**HINT**the increment of the magnetic field induces an emf to the electron placed in the field.this induced emf is due to change in flux. The magnetic flux is a product of magnetic field and area of cross section. We can assign this to the induced emf equation to find the acceleration.

**Complete step by step solution**

According to question we have given that,

Radius of pole face=2.8cm

Minimum value=16.8T

Maximum value=17.2T

Frequency=\[\dfrac{{50}}{\pi }Hz\]

We have to find the amplitude of the electric field induced by the magnetic field variation.

Firstly we can find the change in magnetic field$\left( {\Delta B} \right) = $Maximum value-Minimum value

Therefore, $\Delta B = 17.2 - 16.8 = 0.4T$

We know that the Time period$\left( t \right) = \dfrac{1}{\upsilon }$

Thus, $\dfrac{{\Delta B}}{t} = 0.4 \times \dfrac{{50}}{\pi } = \dfrac{{20}}{\pi }T/s$

The induced emf is given by faraday’s law as:

$e = - \dfrac{{d\phi }}{{dt}}$

and the induced emf can be written in terms of electric field as:

$e = \smallint \vec E.d\vec s$

Thus $\smallint \vec E.d\vec s = - \dfrac{{d\phi }}{{dt}}$

The flux equal to the magnetic field multiplied with the area, where the area is constant and the magnetic field is a function of time, so:

Using this relation,

\[\smallint \vec E.d\vec t = \vec A.\dfrac{{d\vec B}}{{dt}}\]

For, $r < R$

$E \times 2\pi r = \mathop {\pi r}\nolimits^2 \times \dfrac{{\Delta B}}{t}$

$ \Rightarrow \mathop E\nolimits_r = \dfrac{r}{2}\dfrac{{\Delta B}}{t}$

Now at $r = 2cm = \mathop {2 \times 10}\nolimits^{ - 2} m$

Electric field at $r = 0.02m$

$E = \dfrac{{0.02}}{2} \times \dfrac{{20}}{\pi } = \mathop {6.37 \times 10}\nolimits^{ - 2} \mathop {mNC}\nolimits^{ - 1} $

find the amplitude of the electric field(in units of $\mathop { \times 10}\nolimits^{ - 2} \mathop {mNC}\nolimits^{ - 1} $) induced by the magnetic field variation is equal to $\mathop {6.37 \times 10}\nolimits^{ - 2} \mathop {mNC}\nolimits^{ - 1} $

**NOTE**we are using right hand rule to find the direction of the electric field. The acceleration will be in the direction of the electric field. Since we are dealing with electrons.

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