An electron travelling in the same direction that an electric field points initially has a speed of 4.21 ×107 meters per second. If the electric field has a magnitude of 2.28 ×104 N/C, how far does the electron travel before stopping?
m•a=F =e•E,
a =e•E/m,
s =v²/2•a = v²•m/2e•E =
=4.21•10^7)²•9.1•10^-31/2•1.6•10^-19•2.28•10^4 = 0.22 m.
To determine how far the electron travels before stopping, we need to calculate the stopping distance using the given information.
The force experienced by the electron due to the electric field can be calculated using the equation:
F = qE
Where F is the force, q is the charge of the electron, and E is the electric field strength.
The force experienced by the electron is equal to the centripetal force required to maintain the circular motion.
The centripetal force can be calculated using the equation:
F = (m * v^2) / r
Where m is the mass of the electron, v is the velocity of the electron, and r is the distance from the center of the circular path.
Since the electron is moving in the same direction as the electric field, the force experienced by the electron due to the electric field will oppose the motion of the electron. Therefore, the electric force is equal and opposite to the centripetal force.
Setting the two equations equal to each other:
qE = (m * v^2) / r
Rearranging the equation to solve for the stopping distance:
r = (m * v^2) / (qE)
Given:
m = mass of the electron = 9.11 × 10^-31 kg
v = speed of the electron = 4.21 × 10^7 m/s
q = charge of the electron = -1.6 × 10^-19 C
E = electric field strength = 2.28 × 10^4 N/C
Substituting the values into the equation:
r = (9.11 × 10^-31 kg * (4.21 × 10^7 m/s)^2) / (-1.6 × 10^-19 C * 2.28 × 10^4 N/C)
Calculating the stopping distance:
r = 0.1406 meters
Therefore, the electron travels approximately 0.1406 meters before stopping.