Two large conducting parallel plates A and B are separated by 2.4 m.A uniform field of 1500 V/m,in the positive x-direction,is produced by charges on the plates.The center plane at x = 0.00 m is an equipotential surface on which V = 0.An electron is projected from x = 0.00 m,with an initial velocity of 1.0 × 10⁷ m/s perpendicular to the plates in the positive x-direction,as shown in the figure.What is the kinetic energy of the electron as it reaches plate A?
(e = 1.60 × 10^-19 C,m_el= 9.11 × 10^-31 kg)

Question

Quizplus · Accepted Answer

The electric potential energy gained by the electron while moving from the center plane to plate A is given by:
ΔU = qΔV
where q is the charge of the electron and ΔV is the change in electric potential between the two points. 
Since the center plane is an equipotential surface, there is no change in electric potential between the initial and final points. Therefore, ΔV = 0.
Thus, ΔU = 0.
As no external forces act on the electron during its motion, the total mechanical energy (kinetic + potential) of the electron is conserved. Therefore, the kinetic energy gained by the electron while moving from the center plane to plate A is equal to the electric potential energy it loses.
The electric potential energy lost by the electron while moving from the center plane to plate A is given by:
U = qV
where V is the electric potential at the initial point. Since V = 0 at the center plane, U = 0.
Therefore, the kinetic energy gained by the electron while moving from the center plane to plate A is zero.
Hence, the kinetic energy of the electron as it reaches plate A is equal to the initial kinetic energy, which is given by:
KE = (1/2) mv²
where m is the mass of the electron and v is its initial velocity.
Substituting the given values, we get:
KE = (1/2) (9.11×10^-31 kg) (1.0 × 10^7 m/s)² = 4.55 × 10^-17 J
The electron loses all its kinetic energy by the time it reaches plate A as it is moving against the direction of the electric field. Therefore, the answer is given in negative sign as:
KE = -3.3 × 10^-16 J = -3.3 × 10^-16 J.

Two Large Conducting Parallel Plates a and B Are Separated