Consider a negatively charged particle entering a region between two charged pla

Question

Consider a negatively charged particle entering a region between two charged plates, as shown in the diagram below. The initial velocity of the particle is 7.0 x 107 m/s. The mass of the particle is 9.1 x 10-31 kg and the charge is -1.6 x 10-19 C. The distance between the plates is 0.025 m. You can consider the electrical force to be the only force acting between the plates. (The force of gravity is negligible and can be considered to be zero in this problem.)

Determine the magnitude and the direction of the electric field, if the particle just reaches the negative plate (if the velocity at the negative plate is zero). Show your work and explain your reasoning.

Explanation / Answer

using the force of gravity = electrcal force between the plates

such that

ma = Eq

we cna determine electric field E = ma/q

we have m = 9.11 e-31 kgs and

q = 1.6 e-19 C

so

we just need accleration a to find to EF E

so we use eqn of motion as v^2 = 2aS

such that accleration a = v^2/2S

a = (7e7 * 7e7)/( 2* 0.025)

a = 9.8 *10^16 m/s^2

so

finally Electric field E = ma/q

E = 9.11e-31 * 9.8 e16 /1.6 e-19

E = 5.58 *10^5 N/C and this is directed towards the +ve plate

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