g The ball has a mass of 150 grams. If the ball has a positive charge, what initial velocity must it have at the 200-V level for it to reach its maximum height at the 700-V level

u_o = 12.91 m/s

Explanation:

Given:

- mass of the ball m = 0.15 kg

- Spacing between each equipotential line s = 1.0 m

- Charge on the ball is q = 10 mC

Find:

- What initial velocity must it have at the 200-V level for it to reach its maximum height at the 700-V level

Solution:

- Notice that the Electric field lines are directed from Higher potential to lower potential i. e V = + 700 level to V = 200 level. The gravitational acceleration also acts downwards.

- We will compute a resultant acceleration due to gravity and Electric Field as follows:

g' = g + F_e / m

- Where F_e is the Electrostatic Force given by:

F_e = E*q

- Electric field strength is given by:

E = V / d

- Hence,

g' = g + (dV*q / d*m)

- Input values:

g' = 10 + (500*10^-2 / 5*0.15)

g' = 16.6667 m/s^2

- Now use one of the equation of motions in y-direction:

h_max = u_o ^2 / 2*g'

- Input values where h_max = 5 m

5*2*g' = u_o ^2

u_o = sqrt (166.667)

u_o = 12.91 m/s