Question

A small sphere with mass 5*10^-7 kg and charge is released from rest a distance of 0.500 m above a large horizontal insulating sheet of charge that has uniform surface charge density = 8*10^-12 C/m^2 .

Using energy methods, calculate the speed of the sphere when it is 0.150 m above the sheet of charge?

Answer 1

To calculate the speed of the sphere when it is 0.150 m above the charged sheet, energy conservation is used. We consider the conversion of initial electric and gravitational potential energy into kinetic energy plus final potential energy and solve for the sphere's velocity.

Step-by-step explanation:

The problem given involves energy methods in physics, specifically relating to electrostatics and mechanical energy. A small sphere with a given mass and charge is released from rest above a charged sheet. To find the speed when the sphere is at a certain distance above the sheet, one can use the principle of conservation of energy. The initial potential energy (both gravitational and electric) is equal to the final kinetic energy plus the final potential energy.

The steps are as follows:

1. Calculate the initial electric potential energy using the surface charge density of the sheet and the charge on the sphere.
2. Calculate the initial gravitational potential energy using the mass of the sphere, acceleration due to gravity, and height above the sheet.
3. Calculate the final electric and gravitational potential energies when the sphere is at the final height.
4. The initial total potential energy minus the final total potential energy gives us the kinetic energy, from which we can calculate the speed of the sphere.

Answer 2

In your problem where the ask is to calculate the sped of the sphere when it is 0.150m above the sheet where as the small sphere has a mass of 5*10^-7 kg and the charge is release from  a rest distance of 0.5m. The answer to this problem would be 0.0127