A An electric field E is setup between of a capacitor as shown in figu...
Introduction:
In this problem, we are given an electric field E setup between the plates of a capacitor. An electron enters the field between the plates with a velocity v and the length of each plate is L. We need to find the deviation of the path of the electron.
Formula:
The force on a charged particle in an electric field is given by F = qE, where F is the force, q is the charge of the particle, and E is the electric field strength.
Explanation:
The electron enters the electric field between the plates. The force acting on the electron due to the electric field is given by F = qE, where q is the charge of the electron and E is the electric field strength. The force acts perpendicular to the velocity of the electron.
As the force is perpendicular to the velocity of the electron, the path of the electron will be circular. The radius of the circular path can be calculated using the formula:
r = mv/qB
where m is the mass of the electron, v is the velocity of the electron, q is the charge of the electron, and B is the magnetic field strength.
In this problem, there is no magnetic field, so the path of the electron will be a straight line. The deviation of the path of the electron can be calculated using the formula:
d = (1/2)qEL^2/mv^2
where d is the deviation of the path, q is the charge of the electron, E is the electric field strength, L is the length of each plate, m is the mass of the electron, and v is the velocity of the electron.
Result:
The deviation of the path of the electron is given by d = (1/2)qEL^2/mv^2.