A very large flat metal plate is kept at potential V_1 = 400 Volts. A metal sphe
ID: 1642468 • Letter: A
Question
A very large flat metal plate is kept at potential V_1 = 400 Volts. A metal sphere of radius R = 20 cm is located next to the plate and is kept at potential V_2 = +1000 Volts. The center of the sphere is L = 22 cm away from the plate. Due to some physical processes (which we don't need to worry about) an electron emerges on the surface of the plate at point B: it has speed v_1 = 1.00 times 10^7 m/s and direction as shown on the picture. Assume there is vacuum between the sphere and the plate, so there are no other particles to hit. a) What is the speed of electron v_2 when it hits the sphere? b) If instead it were an anti-electron (same charge as electron, but positive) with the same velocity, would it be able to reach the sphere? Why?Explanation / Answer
deltaKE = -q deltaV
m (vf^2 - vi^2) / 2 = -q (VA - VB)
(a) (9.109 x 10^-31)[ v^2 - (1 x 10^7)^2] / 2 = -(-1.6 x 10^-19) (1000 - 400)
v^2 - 10^14 = 2.11 x 10^14
v = 1.76 x 10^7 m/s
(b) (9.109 x 10^-31)[ v^2 - (1 x 10^7)^2] / 2 = -(1.6 x 10^-19) (1000 - 400)
v^2 - 10^14 = - 2.11 x 10^14
v^2 = -1.1 x 10^14
v^2 cannot be negative. that means it will not reach to sphere.
because it does not have sufficient Kinetic energy .
to reach that sphere,
KE >= magnitude of change in PE