A very small object with mass 7.50×10−9 kg and positive charge 7.30×10−9 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. What initial speed must the object have in order for its closest distance of approach to the sheet to be 0.100 m?

To solve this problem we will start by calculating the electric field. This can be defined as the change in charge density over twice the permittivity constant in a vacuum. From this value we will proceed to calculate by the relations of energy and load, the relation with the speed and the position of the objective.

Our values,

The electric field due to very large insulating sheet can be calculated as

The relation between the electric field E and potential V is given by,

Therefore, the potential in terms of electric field can be written as,

The kinetic energy of the object is given by

The speed of the object then is

Replacing we have then,

Therefore the initial speed is 48.3322m/s

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.