Help with 3 Electro-Exercises: Q, R, r, v, q

[claudiadeluca]

The physical terms might not be the right english ones, I am not english. I hope you will understand anyway. I need help with the 3 following exercises, if anyone could dedicate some time to them I would be really grateful. Thank you.

1) Determine the electric and potential fields in all the space for a system composed of a sphere of radius=R, equally charged with charge=Q, surrounded by a spherical conductor crown with internal radius=R and external radius=r.

2) A proton is fired toward another proton, which is steady at a great distance, with speed v= 2.4 * 10^8 m/s. Find the minimal distance between the two protons.

3) We have a vertical electric field. How intense must it be and what direction must it have to hold a particle in equilibrium? The particle has mass = 10^-8 g and is charged with q= 1.7 * 10^-9 C.

Thank you very much in advance.

 

[lpfr]

1- 1- I do not understand the geometry of the problem. What is the shape of the crown? Are there simply two concentric spheres?
2- Move to the frame of the center of mass of the two protons. Compute the kinetic energy of both. Compute the distance at which the potential energy is equal to the original kinetic energy. Beware! the speed is relativistic. The CM and the energy must be calculated with the relativistic formulas.
3- The force of the particle is qE and must be equal to the weigh of the particle.