Question

A very small object with mass 8.30×10⁻⁹ kg and positive charge 7.00×10⁻⁹ C is projected directly toward a very large insulating sheet of positive charge that has uniform surface charge density 5.90×10−8C/m2. The object is initially 0.460 m from the sheet.

A. What initial speed must the object have in order for its closest distance of approach to the sheet to be 0.230 m ?

Express your answer to three significant figures and include the appropriate units.

Answer 1

Electric potential difference between two points near a infinite sheet = V

V = d/ Here is surface charge density = 5.9*10^-8

=8.85*10^-12 , d = distance between two points = (0.46 - 0.23) = 0.23 m

Putting the values V = 1533.33

Difference in potential energy = U = qV , here q is charge

U = 1.073*10^-5 joule

Now , using conservation of energy :

Change in potential energy = change in kinetic energy

Change in kinetic energy = 0.5mv²

1.0733*10^-5 = 0.5*8.3*10^-9v²

v² = 2586.26

v = 50.86 m/sec