2. (WRH-7, #2246) An electron is launched at a 40° angle and a speed of 2.0 * 10

Question

2. (WRH-7, #2246) An electron is launched at a 40° angle and a speed of 2.0 * 106 m/s from a point A on x-axis. It moves through a uniform electric field E = ( 5.00 A screen for detecting electrons is positioned parallel to the y-axis at a distance x = 3.00 cm from the starting point. In unit-vector notation, what is the velocity of the electron when it hits the vertical plate? 3, (Kn #29.42) A proton and -particle (q = +2e, m = 4u) are fired directly toward each other from f away, each with an initial speed of 0.01c. What is their distance of closest approach, as measured between their centers ? (Armin if g = v, ; ,min-1.93 * 10-14 m, v 1.8*106 m/s) 4. Is this assembly stable? Why or why not. Expalin it. (1) Explain why or why not in terms of the work done by some forces to bring the charges from infi to that position.? (2) Explain why or why not in terms of the energy the system has right now in comparison to the en the system has when all the charges were infinitely far from each other. Take potential energy as ZERO at infinitely far distance

Explanation / Answer

2. givne theta = 40 deg

v = 2*10^6 m/s

E = 5 N/C

the particel is electron

electric field is towards +y axis, so the force is towards -ve y axis

x = 3 cm

in unit vector notation, velocity of particel when it hits the platge

v = vxi + vyj

vx = v*cos(40)

-2*qE*x/m = vy^2 - v^2*sin^2(40)

q = 1.6*10^-19 C

m = 9.1*10^-31 kg

hence

vy = 1.2648938*10^6 m/s

hence

v = 1.53208888*10^6 i + 1.2648938*10^6 j m/s

3. given

proton

q1 = e

m1 = 1.6*10^-27 kg

, and alpha particel

q2 = 2e

m2 = 4m1

initial speed, u = 0.01 c each

distance of closest approach = d

from conservation of energy

0.5(m1 + m2)u^2 = kq1*q2/d

hence

d = 2k*q1q2/(m1 + m2)*u^2

d = 1.277155*10^-14 m

4. a. work done to bring two positive charges from infinity to close together is +ve hencem the resultant assembly is not stable

b. as potential energy of new assembly is greater than the old state, the new assembly is unstable

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