8. A mixture of 2 different powdered minerals can be separated in the laboratory by using an electric field. The mixture to be separated is furst placed in a vibrating tray in which the two types of powdered minerals become oppositely charged by friction. The tray has a small opening through which the minerals fall vertically from rest through a constant horizontal electric field set up between a pair of charged parallel plates. The following figure shows a possible setup. powdered mineral mixture vibrating tray 10.0 cm OV +100 KV Mineral A Mineral B In the above setup, a potential difference of 100 k V is maintained between the two large parallel plates which are separated horizontally by a distance of 15.0 cm. After falling through the plates, the minerals are separated by a horizontal distance of 10.0 em and collected in two exclusive containers finally The individual grains of the powdered minerals can be modeled as spheres of diameter 100 umm, each canying a charge of magnitude 1.60 x 10"C. (You may assume that air resistance and upthrust are negligible.) (i) Determine the magnitude of the force on a grain due to the electric field produced by the two large parallel plates. (ii) Calculate the electrical force between two charged mineral grains that are adjacent to each other. (mii) Given that the magnitude of charge per unit mass of the minerals is 2.00x10- C kg calculate the magnitude of the horizontal acceleration of each mineral grain. (You can exclude the electric force between two charged mineral grains which are adjacent to each other in your formulation ) (iv) Calculate the time taken for the minerals to pass out of the parallel plates. (To pass out of the parallel plates you can assume that the minerals have to move a horizontal distance of 5 cm either to the left or to the right from the center of the vibrating tray. You do not have to consider the vertical height of the plates.)