An electron is traveling at 2.3 *10^3m/s, enters perpendicular to the electric field between two horizontal charged parallel plates. If the electric field strength is 1.5*10^2V/m calculate the time taken for the electron to deflect a distance of 1.0*10^-2 toward the positive plate. Ans: 2.8*10^-8s
speed << speed of light so forget special relativity
F = q E = 1.6*10^-19 * 1.5*10^2
a = F/m = 1.6 * 10^-19 * 1.5*10^2 / (9.1 * 10^-31)
= (1.6*1.5 / 9.1) * 10^14 m/s^2 = 0.264 * 10^14
d = (1/2) a t^2
10*-2 = 0.132 * 10^14 t^2
t^2 = (1/0.132) * 10^-16
t = sqrt(7.58) * 10^-8 = 2.75 *10^-8 seconds,
not long but it goes (2.3*10^3) (2.75*10^-8) = 6.3 * 10^-5 meters forward during that time
To calculate the time taken for the electron to deflect a distance of 1.0*10^-2 meters toward the positive plate, we can use the equation relating force, charge, and electric field:
F = qE
Where:
F is the force experienced by the electron,
q is the charge of the electron,
and E is the electric field strength.
Since the electron has a negative charge, the force it experiences will be in the opposite direction to the electric field. Therefore, we can write:
F = -qE
The force experienced by the electron can also be expressed as the rate of change of momentum:
F = dp/dt
Where:
dp is the change in momentum of the electron,
and dt is the time taken for this change in momentum.
We know that momentum (p) can be calculated as the product of mass (m) and velocity (v):
p = mv
To convert the given velocity from meters per second to meters per unit time, we divide it by the displacement per unit time (which is 1 meter in this case):
v = 2.3 * 10^3 m/s / 1 m = 2.3 * 10^3 m/s
Since we already have the velocity, we can calculate the momentum (p):
p = mv = (9.11 * 10^-31 kg) * (2.3 * 10^3 m/s) = 2.0943 * 10^-27 kg m/s
Now, we can find the force experienced by the electron using the equation F = dp/dt:
- qE = (2.0943 * 10^-27 kg m/s) / dt
Rearranging the equation to solve for dt:
dt = (2.0943 * 10^-27 kg m/s) / (-qE)
Substituting the given values for charge (q) and electric field strength (E):
dt = (2.0943 * 10^-27 kg m/s) / (1.6 * 10^-19 C * 1.5 * 10^2 V/m)
Evaluating the expression:
dt = (2.0943 * 10^-27 kg m/s) / (2.4 * 10^-17 C V/m)
dt = 8.72625 * 10^-11 s
Therefore, the time taken for the electron to deflect a distance of 1.0 * 10^-2 meters toward the positive plate is approximately 8.73 * 10^-11 seconds, which is not equal to the given answer of 2.8 * 10^-8 seconds. There may be a calculation error or the given answer may be incorrect.
To calculate the time taken for the electron to deflect a distance of 1.0*10^-2m, we need to use the equation of motion for a charged particle in an electric field.
The equation is given by:
d = (1/2) * (a * t^2)
Where:
d is the distance traveled by the electron (1.0*10^-2m),
a is the acceleration of the electron (which is due to the electric field),
and t is the time taken for the electron to travel that distance.
Now, we know that the acceleration of a charged particle in an electric field is given by:
a = (q * E) / m
Where:
q is the charge of the electron (-1.6*10^-19 C),
E is the electric field strength (1.5*10^2 V/m),
and m is the mass of the electron (9.11*10^-31 kg).
Substituting these values into the equation, we get:
1.0*10^-2 = (1/2) * ((-1.6*10^-19 C * 1.5*10^2 V/m) / 9.11*10^-31 kg) * t^2
Now we can rearrange the equation to solve for t:
t^2 = (2 * 1.0*10^-2 * 9.11*10^-31 kg) / (1.6*10^-19 C * 1.5*10^2 V/m)
t^2 = 1.20 * 10^-30 kg * m^2 / (C * V)
t^2 = 1.20 * 10^-30 kg * m^2 / (C * J/C)
t^2 = 1.20 * 10^-30 kg * m^2 / J
Now, we can calculate the value of t by taking the square root:
t = sqrt(1.20 * 10^-30 kg * m^2 / J)
t = 3.46 * 10^-16 s
Therefore, the time taken for the electron to deflect a distance of 1.0*10^-2m is approximately 3.46 * 10^-16 seconds, which is the same as 3.46 * 10^-16 seconds.