Question

A direct current flowing through the winding of a long cylindrical solenoid of radius r produces a uniform magnetic induction B in it. An electron traveling at velocity v enters into the solenoid along the radial direction between its turns at right angles to the solenoid axis. After a certain time, the electron, deflected by the magnetic field, leaves the solenoid. Calculate the time which the electron spends inside the solenoid.

Answer 1

The time an electron spends inside a solenoid can be calculated using the radius of the circular path it follows in the magnetic field and its velocity, applying the half period of circular motion formula.

Step-by-step explanation:

To calculate the time an electron spends inside a solenoid when traveling at a velocity v perpendicular to the solenoid's axis and subjected to a uniform magnetic induction B, we apply the principles of circular motion in a magnetic field. The magnetic force acting on an electron in a magnetic field is given by the Lorentz force, F = q(v x B), where q is the charge of the electron and v is its velocity. Since the electron is moving at a right angle to the field lines, the path it follows is a circle with radius r determined by the equation m(v^2)/r = q(vB), where m is the mass of the electron.

The time t to complete half a circle within the solenoid and exit is given by the half period of circular motion: t = πr/v, where r is the radius of the circular path. Substituting the expression for the radius, we get t = πm/qB. This time in milliseconds (ms) gives the duration the electron spends inside the solenoid before being deflected out.