Question

PROBLEM3. A proton is fired with a speed of 200,000m's from the midpoint of a capac A) Show that this is an insufficient speed to reach the positive plate itor which has a potential of oVion the negative plate (left hand side) and 500 V on the positive piaie B) How fast is it going when it hits thenegative plate?- 500 V iGURE P29.48

Answer 1

The problem can be solved from conservation of energy approach

A) potential at midpoin = 500/2=250V

electrical potential energy of proton = 1.6*10^-19*250=4*10^-17 Joule

mass of proton = 1.67*10^-27 kg

initial speed = 2*10⁵ m/s

Kinetic energy of proton = (1/2)mv² = (1/2)*1.67*10^-27*(2*10⁵)² = 3.34*10^-17 Joule

Total initial energy of proton =4*10^-17 +3.34*10^-17 = 7.34*10^-17 Joule

For the proton to reach positive plate,minimum toatl inital energy needed of proton = 500*1.6*10^-19 = 8*10^-17 Joule

The total inital energy of proton is less than the energy required to reach positive plate.Therefore, proton cannot reach positive plate

b)When it hits the negative plate,there is not voltage at plate and hence electric potential energy of proton will be zero at negative plate. The entire initial energy will be converted into kinetic energy

Let the speed at which it will hit negative plate be v

(1/2)mv² = 7.34*10^-17

v = 296486.4 m/s