To find the acceleration of the electron in the given electric field, we can use the equation of motion for a charged particle in an electric field.
Given:
Initial velocity of the electron, v_initial = 1 × 10^6 m/s (in the x-direction)
Electric field, E~ = (360 N/C) ˆj (in the y-direction)
Fundamental charge, e = 1.602 × 10^(-19) C
Mass of the electron, m = 9.109 × 10^(-31) kg
The force experienced by a charged particle in an electric field is given by the equation:
F~ = qE~
Where:
F~ is the force vector,
q is the charge, and
E~ is the electric field vector.
Since the electron has a negative charge, the force vector F~ will be in the opposite direction of the electric field vector E~.
The force acting on the electron can be calculated as:
F~ = -qE~
Substituting the values:
F~ = -(1.602 × 10^(-19) C) × (360 N/C) ˆj
Now, we can use Newton's second law of motion, F~ = ma~, to find the acceleration of the electron.
Since the force acting on the electron is in the y-direction (opposite to the electric field direction), and the mass of the electron is known, we have:
F_y = ma_y
Substituting the force in the y-direction:
-(1.602 × 10^(-19) C) × (360 N/C) = (9.109 × 10^(-31) kg) × a_y
Solving for a_y:
a_y = -[(1.602 × 10^(-19) C) × (360 N/C)] / (9.109 × 10^(-31) kg)
Calculating the value:
a_y ≈ -6.56 × 10^11 m/s^2
The acceleration of the electron is approximately -6.56 × 10^11 m/s^2 in the y-direction. Note that the negative sign indicates that the acceleration is opposite to the direction of the electric field, as expected for a negatively charged particle.