An electron with initial speed = 2.54×10^7 m/s is traveling parallel to an electric field of magnitude = 1.66×10^4 N/C .
How much time will elapse before it returns to its starting point?
To find the time it takes for the electron to return to its starting point, we can use the equation for the motion of a charged particle in an electric field.
The force experienced by a charged particle in an electric field is given by the equation:
F = qE
where F is the force, q is the charge of the particle, and E is the electric field strength.
The force experienced by an electron is opposite in direction to the electric field, so the equation becomes:
F = -qE
The force acting on the electron is provided by the electric field, and it is equal to qE. The magnitude of the force is given by:
|F| = qE
The magnitude of the force acting on the electron is also equal to the mass of the electron multiplied by its acceleration:
|F| = m * a
where m is the mass of the electron and a is its acceleration.
Since the force acting on the electron is due to the electric field, we can equate the two equations:
qE = m * a
Since the acceleration of the electron is equal to the change in velocity divided by the time taken, we can rewrite the equation as:
qE = m * (Δv / Δt)
Rearranging the equation, we get:
Δt = m * (Δv / (qE))
The change in velocity, Δv, is the final velocity minus the initial velocity. In this case, the electron returns to its starting point, so the final velocity is equal to the negative of the initial velocity:
Δv = -2.54×10^7 m/s - 2.54×10^7 m/s = -5.08×10^7 m/s
To find the time it takes for the electron to return to its starting point, we need to know the mass of the electron (m) and the charge of the electron (q). The mass of an electron is approximately 9.1×10^-31 kg, and the charge of an electron is approximately -1.6×10^-19 C.
Substituting the values into the equation, we get:
Δt = (9.1×10^-31 kg) * (-5.08×10^7 m/s) / (-1.6×10^-19 C * 1.66×10^4 N/C)
Simplifying the equation, we get:
Δt = 1.04×10^-14 s
Therefore, it will take approximately 1.04×10^-14 seconds for the electron to return to its starting point.