An electron, travelling at 2.3*10^ 3 m/s , enters perpendicular to the electric field between two horizontal charged parallel plates. If the electric field strength is 1.5*10^ 2 V/m. , calculate the time taken for the electron to deflect a distance of 1.0 * 10 ^ - 2 * m toward the positive plate. Ignore gravita tional effects.
F = Q E = m a
so
1.6*10^-19 * 1.5*10^2 = 9.1*10^-11 * a
solve for a
distance = 10^-2 = (1/2) a t^2
solve for t
Well, first of all, let me just say that this electron seems to have some serious navigation skills! It's as if it's part of the Electric Field Flying Circus!
Now, let's get down to business. To calculate the time taken for the electron to deflect a distance of 1.0 * 10^(-2) m, we need to consider a few things. The force experienced by the electron due to the electric field can be calculated using the formula F = qE, where F is the force, q is the charge of the electron, and E is the electric field strength.
Since the force is perpendicular to the initial velocity of the electron, it won't affect its speed, but it will cause the electron to change direction. This means that the time taken for the electron to deflect the distance will depend on its initial velocity.
To calculate the time taken, we need to determine the time taken for the electron to travel the distance on the x-axis. Since the electron is moving perpendicularly to the electric field, it won't be affected in the vertical direction. Thus, only the horizontal distance needs to be considered.
Using the formula t = d/v, we can calculate the time taken. Plugging in the values, we get t = (1.0 * 10^(-2) m) / (2.3 * 10^(3) m/s), which gives us approximately 4.35 * 10^(-6) seconds.
So, it takes the electron about 4.35 microseconds to deflect a distance of 1.0 * 10^(-2) m toward the positive plate. Just enough time for a quick joke! Why was the electron so good at basketball? Because he knew how to charge the net! Keep sparking curiosity!
To calculate the time taken for the electron to deflect a distance of 1.0 * 10^-2 m toward the positive plate, we can use the equation:
F = q * E
Where:
F is the force experienced by the electron,
q is the charge of the electron (1.6 * 10^-19 C),
E is the electric field strength (1.5 * 10^2 V/m).
The force experienced by the electron can be rewritten as:
F = m * a
Where:
m is the mass of the electron (9.11 * 10^-31 kg),
a is the acceleration of the electron.
Since the electron is initially traveling perpendicularly to the electric field, the force experienced by the electron will cause it to accelerate towards the positive plate. Thus, the acceleration can be calculated using the equation:
a = F / m
Substituting the values into the equations:
F = q * E
F = (1.6 * 10^-19 C) * (1.5 * 10^2 V/m)
F = 2.4 * 10^-17 N
a = F / m
a = (2.4 * 10^-17 N) / (9.11 * 10^-31 kg)
a = 2.64 * 10^13 m/s^2
Now, we can calculate the time taken for the electron to deflect the given distance using the equation:
s = ut + (1/2) * a * t^2
Where:
s is the distance deflected by the electron (1.0 * 10^-2 m),
u is the initial velocity of the electron (2.3 * 10^3 m/s),
a is the acceleration of the electron (2.64 * 10^13 m/s^2),
t is the time taken.
Rearranging the equation:
t = sqrt((2s)/a)
Substituting the values and calculating:
t = sqrt((2 * (1.0 * 10^-2 m)) / (2.64 * 10^13 m/s^2))
t = sqrt(7.576 * 10^-16 s^2 / m^2)
t = 8.70 * 10^-9 s
Therefore, the time taken for the electron to deflect a distance of 1.0 * 10^-2 m toward the positive plate is approximately 8.70 * 10^-9 seconds.
To calculate the time taken for the electron to deflect, we can use the equation for the force on a charged particle in an electric field:
F = q * E
Where:
F is the force on the electron (unknown)
q is the charge of the electron (1.6 * 10^-19 C)
E is the electric field strength (1.5 * 10^2 V/m)
First, we need to calculate the force acting on the electron:
F = q * E
= (1.6 * 10^-19 C) * (1.5 * 10^2 V/m)
= 2.4 * 10^-17 N
The force acting on the electron causes its acceleration:
F = m * a
Where:
m is the mass of the electron (9.1 * 10^-31 kg)
a is the acceleration of the electron (unknown)
Rearranging the equation, we can solve for acceleration:
a = F / m
= (2.4 * 10^-17 N) / (9.1 * 10^-31 kg)
= 2.64 * 10^13 m/s^2
Next, we use the equation for displacement:
s = ut + (1/2) * a * t^2
Where:
s is the displacement of the electron (1.0 * 10^-2 m)
u is the initial velocity of the electron (2.3 * 10^3 m/s)
a is the acceleration of the electron (2.64 * 10^13 m/s^2)
t is the time taken (unknown)
We rearrange the equation and solve for time:
t = sqrt((2s) / a)
= sqrt((2 * 1.0 * 10^-2 m) / (2.64 * 10^13 m/s^2))
= sqrt(7.57 * 10^-16 s^2 / m^2)
= 8.7 * 10^-9 s
Therefore, the time taken for the electron to deflect a distance of 1.0 * 10^-2 m toward the positive plate is approximately 8.7 * 10^-9 seconds.