1. A uniformily charged thin ring has radius 15.0 cm and total charge of -20.0 n

Question

1. A uniformily charged thin ring has radius 15.0 cm and total charge of -20.0 nC. A proton (mp=1.67*10^-27 kg) is placed on the ring's axis a distance 30.0 cm from the center of the ring and is constrained to stay on the axis of the ring. The proton is then released from rest. A) what is the speed of the proton when it is 10.0 cm from the center of the ring. B) what is the acceleration of the proton when it is 10.0 cm from the center of the ring? 2. A small 15.0 g + 3.00 uC particle is projected with an initial speed of 20.0 m/s toward a very large uniformily charged plane of charge of surface density ?=2.00 mC/m^2 . A particle stops momentarily when it is 5.00 cm away from the plane A) how far from the line of charge the particle was projected? B) what is the potential difference between the point where charged particle was initially projected and where it stopped? 1. A uniformily charged thin ring has radius 15.0 cm and total charge of -20.0 nC. A proton (mp=1.67*10^-27 kg) is placed on the ring's axis a distance 30.0 cm from the center of the ring and is constrained to stay on the axis of the ring. The proton is then released from rest. A) what is the speed of the proton when it is 10.0 cm from the center of the ring. B) what is the acceleration of the proton when it is 10.0 cm from the center of the ring? 2. A small 15.0 g + 3.00 uC particle is projected with an initial speed of 20.0 m/s toward a very large uniformily charged plane of charge of surface density ?=2.00 mC/m^2 . A particle stops momentarily when it is 5.00 cm away from the plane A) how far from the line of charge the particle was projected? B) what is the potential difference between the point where charged particle was initially projected and where it stopped? 2. A small 15.0 g + 3.00 uC particle is projected with an initial speed of 20.0 m/s toward a very large uniformily charged plane of charge of surface density ?=2.00 mC/m^2 . A particle stops momentarily when it is 5.00 cm away from the plane A) how far from the line of charge the particle was projected? B) what is the potential difference between the point where charged particle was initially projected and where it stopped?

Explanation / Answer

1. V = k Q / sqrt(R^2 + d^2)

Applying energy conservation,

PEi + KEi = PEf + KEf

(1.6 x 10^-19)(9 x 10^9 x -20 x 10^-9 / sqrt(0.15^2 + 0.30^2)) + 0 = (1.6 x 10^-19)(9 x 10^9 x -20 x 10^-9 / sqrt(0.15^2 + 0.10^2)) + (1.67x 10^27 v^2 / 2)

v = 2.97 x 10^5 m/s

(B) E = k Q d / (d^2 + R^2)^(3/2)

E = (9 x 10^9)(20 x 10^-9)(0.10) / (0.10^2 + 0.15^2)^(3/2)

E = 3072 N/C

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