Question

3.6.1 Let’s take some baby steps. Step 1: Replace wire with
single point charge.
You and a friend have been given the task of designing a display for the Physics building that will demonstrate the strength of the electric force. Your friend comes up with an idea that sounds neat theoretically, but you are not sure it is practical. She suggests you use an electric force to hold a marble in place on a sloped plywood ramp. She would get the electric force by attaching a different but suitably small charged sphere firmly somewhere near the bottom of the ramp along the perpendicular line starting from the first marble. She claims that if the charges on the marble and ring and the slope of the ramp are chosen properly, the marble would be balanced at some distance from the sphere. To test this idea, you decide to calculate the necessary amount of charge on the marble for a reasonable ramp angle of 15 degrees and a distance of 10 cm from a sphere charged with 800 microcoulombs. The marble would roll in a slot cut lengthwise into the center of the ramp. The mass of the lightest marble you can find is 25 grams.

Answer 1

The gravitational force acting on a slanted ramp is given by

This force must be balanced by the Culombic attrection.

Culombic attraction between two charged bodies is given by

Given that m = 25 g = 0.025 kg

and = 15 degrees,

Given that q = 800*10^-6 C

r = 10 cm = 0.1 m,

When

Since the sphere was charged to a much higher value, this should be easily possible. In actual case, this should be easier since there will be effect of friction on the table, which will reduce the motion of the marble