- #1
Saitama
- 4,243
- 93
Homework Statement
Homework Equations
The Attempt at a Solution
At any instant in the circular region, let the horizontal and vertical components of velocity of electron be ##v_x## and ##v_y##. Let the origin be at the point from where the electron enters the magnetic field. Positive x-axis is in horizontal direction to left and positive y-axis in vertically upward direction.
The force acting on the electron is
[tex]F=q\vec{v}\times \vec{B}[/tex]
[tex]F=q(v_x\hat{i}+v_y\hat{j}) \times (B\hat{-k})[/tex]
[tex]\Rightarrow F=qv_yB\hat{i}+qv_xB\hat{j}[/tex]
From the above equation, ##dv_x/dt=qv_yB## and ##dv_y/dt=qv_xB##
As ##v_x^2+v_y^2=v^2##, hence ##v_xdv_x=-v_ydv_y##. If I substitute for ##dv_x## and ##dv_y##, I end up proving ##1=1##.
Any help is appreciated. Thanks!