Question

An electron having 500ev energy enters at right angle to a uniform magnetic field of 10^-4 Tesla. If its specific charge is 1.75×10^11. Calculate radius of its circular orbit.​

Answer 1

Answer:

The correct answer might be $r = 2.8^{27}$ meters.

Explanation:

The Answer Given might not be correct, I just did what my brain said.

As the angle is perpendicular so Θ=90.

Putting this in the equation to calculate the magnetic force as:

F = evBsinΘ

F= evBsin90                   *sin90 = 1 so,

F= evB.

Now when the electron will start to move in  a circle, The necessary force that makes the electron rotate in a circle is given by Centripetal force.

So,

    Magneteic Force = Centripetal Force

    evB = $\frac{mv^{2} }{r}$

    r = $\frac{mv}{Be}$ ......(1)

Now the problem is, We don't know " v " so we need to calculate velocity first,

Calculation of Velocity:

                                   In order to calculate the velocity of electron, We should know the potiential difference with which the electrons are accelerated which in our case is 500ev. If "V" is the potiential difference, the energy gained by electrons during accelreation will be Ve. This appear as kinectic enrgy of electrons as,

         

                        K.E = Ve

                        $\frac{1}{2}$m$v^{2}$ = Ve

                        v =  $\sqrt{\frac{2ve}{m} }$................(2)

Putting value of velocity in equation 2 from 1:

r = $\frac{mv}{Be}$  $\sqrt{\frac{2ve}{m} }$

$r = \sqrt{\frac{2mev}{Be}}$

$r = \sqrt{\frac{(2)(9.1^{-31})(500) (1.6^{-19} ) }{ (1.75^{11} ) (10^{-4} ) } }$

$r = 2.8^{27}$ meters.