You and a friend have been given the task of designing a display for the Physics

Question

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're 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 uniformly charged semicircular wire near the bottom of the ramp, laying the wire flat on the ramp with each of its ends pointing straight up the ramp. 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 midway between the ends of the wire. 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 semicircle of radius 10 cm with a charge of 800 micro-coulombs. 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

Explanation / Answer

Electric field due to a semi-circle is given by E=2k*lambda/R

lambda=charge per unit length

so,

We need to equate the two forces acting on the marble, i.e. the gravitational force and the electrostatic forces acting on the marble.so,

mgsin(15)=qE

or 25*10^-3*9.81*0.2588=q*(2*9*10^9*800*10^-6/(pi*0.1^2)

or q=1.38*10^-10 C

do tha charge on the mable required is 1.38*10^-10 C

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