electricity in physics problems?

Question

Please show how, thank you in advance :)

1) a 4g object, with a charge of 20 microC on it, accelerates from rest through a potential difference, and afterwards, is moving at 2m/s, What is the potential difference ?

2)find the potential difference necessary when 200 J of work are needed to push a 1microC charge into an electric field

3)what potential difference is needed to give a +3 charge ion a KE of 50 MEV?

4) a charged metal sphere of radious 8 cm has a potential of -500v. with what velocity must an electron be fired toward the sphere if it is to just barely reach the sphere, when started from a position 15cm from the center of the sphere

Answer 1

1)Pe=Ke
Pe=Vq
Ke=.5 m V^2

V=Pe/q=(mv^2)/(2 q)
V=4e-3 (2)^2 / ( 2 x 20E-6)=400Volts

2)V=E/q= 200/1E-6=200,000,000V

3) Ke= 50E6 eV
V=Ke/q=50E+6 eV x1 eV = 1.602 E−19 Joul /[ 3 (1.602 E−19 C )]
V=50E+6 /3=16.7 E+6 Volts

4)S=vt= (15-8) cm
F=Vq/S
a=F/m
S=.5at^2
t=sqrt(2S/a)
t=sqrt(2S/(F/m))
t=sqrt(2S/(Vq/ (S m)))
t=sqrt(2S^2 m/ Vq ))
v=S/t =S/sqrt(2S^2 m/ Vq))
v=sqrt(S^2 V q/2S^2 m))
v=sqrt(Vq/(2m))
m=9.109 E–31 kg
q=1.602 E-19 C
v=sqrt(-500 x -1.602 E-19 /(2 x 9.109 E–31 ))= 6.63 E6 m/s
A bit too fast

Answer 2

4)
R = 0.15 m
Ro = 0.08 m
Vo = -500 V
Me = 511 keV / c² <- mass of electron
c = 298,000 km/s

Electric field E(r) of charged sphere:

E(r) = Eo/(r/Ro)² = EoRo² / r²

Potential of charged sphere is
dP(r) = E(r) dr
V(r) = integral of dP(r) = integral of EoRo² dr / r²
= Vo Ro/r

When electron moves from R = 0.15 m to Ro = 0.08,
its potential energy increases from eV(R) to eV(Ro).
Conservation of energy:

P + K = Po
eV(R) + mV²/2 = eV(Ro)
mV²/2 = e (V(Ro) - V(R))
mV² = 2e Vo(1 - Ro/R)


Answer:
V = √(2eVo/m (1 - Ro/R)) =
= √(2 x 500eV x (1 - 8/15) / 511,000 eV ) x c =
= 0.03 c = 9,000 km/s