An electron iwth an initial speed of 500,000 m/s is brought to rest by an electric field.
(a) Did the electron move into a region of higher potential or lower potential?
(b) What was the potential difference that stopped the electron?
To determine the answers to these questions, we need to analyze the relationship between the speed of the electron and the electric potential.
(a) Did the electron move into a region of higher potential or lower potential?
When an electron is brought to rest by an electric field, it means that the electron has lost all of its kinetic energy. In other words, the electric field does work on the electron, converting its kinetic energy into potential energy. By the conservation of energy, the potential energy gained by the electron must be equal to the kinetic energy it lost.
Since the electron loses kinetic energy, it must be moving from a region of higher electric potential to a region of lower electric potential. Therefore, the electron moves into a region of lower potential.
(b) What was the potential difference that stopped the electron?
To find the potential difference, we can equate the initial kinetic energy of the electron to the final potential energy it gained.
The kinetic energy (KE) can be calculated using the formula:
KE = 0.5 * mass * velocity^2
Plugging in the values:
KE = 0.5 * (9.11 × 10^-31 kg) * (500,000 m/s)^2
KE = 0.5 * (9.11 × 10^-31 kg) * (2.5 × 10^11 m^2/s^2)
KE ≈ 1.14 × 10^-20 J
The electric potential energy (PE) can be calculated using the formula:
PE = charge * potential difference
In this case, the charge of an electron is -1.6 × 10^-19 C, and the potential difference is what we want to determine.
Equating the kinetic energy to the potential energy:
PE = KE
-1.6 × 10^-19 C * potential difference = 1.14 × 10^-20 J
Solving for the potential difference:
potential difference = (1.14 × 10^-20 J) / (-1.6 × 10^-19 C)
potential difference ≈ -7.13 V
Therefore, the potential difference that stopped the electron is approximately -7.13 Volts. Note that the negative sign indicates that the potential difference is more negative, or lower in potential, on the side where the electron comes to a stop.
To determine whether the electron moved into a region of higher or lower potential, we need to understand the relationship between electric potential and the movement of charges.
(a) If the electron is brought to rest, it means that it loses its kinetic energy to the electric field. The potential energy associated with the electron decreases as it moves in the direction of the electric field. This implies that the electron moved into a region of lower potential.
(b) To calculate the potential difference that stopped the electron, we need to use the electric potential energy equation:
Electric Potential Energy (PE) = Charge (q) x Electric Potential Difference (V)
Since the electron loses all its kinetic energy, its final kinetic energy is zero. Therefore, its electric potential energy equals the initial kinetic energy:
PE = initial Kinetic Energy
The initial kinetic energy can be calculated using the equation:
Kinetic Energy (KE) = 0.5 x mass (m) x velocity^2 (v^2)
Substituting the given values:
KE = 0.5 x (mass of electron) x (initial velocity)^2
By equating the initial kinetic energy to the electric potential energy, and solving for the electric potential difference:
PE = qV
0.5 x (mass of electron) x (initial velocity)^2 = qV
V = (0.5 x (mass of electron) x (initial velocity)^2) / q
The mass of an electron (m) is approximately 9.11 x 10^-31 kg, the initial velocity (v) is 500,000 m/s, and the charge of an electron (q) is -1.6 x 10^-19 C.
Now, we can plug in the values to calculate the potential difference (V).
If the initial KE was absorbed by the system, its PE is higher.
Vq=KE change.
solve for V