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1. Homework Statement
2. Homework Equations
3. 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 xaxis is in horizontal direction to left and positive yaxis 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!
2. Homework Equations
3. 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 xaxis is in horizontal direction to left and positive yaxis 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!
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