You have been tasked by the supreme leader to design a launch system capable of

Question

You have been tasked by the supreme leader to design a launch system capable of accelerating a plastic coffee stirrer (stolen from Starbucks) length L = 6.0cm. After cogitation, you decide to charge the stirrer by triboelectricity, giving it a uniform charge Q = 10 nC. You then hold it close to a long charged wire, linear charge density lambda_w = 1.0 times 10^-7 C/m. The stirrer is initially at a distance of d = 2.0 cm for the wire. You let it go and it indeed shoot away, validating your design. a) Explain qualitatively and carefully why the stirrer is repelled. b) Calculate the net electric force on the stirrer at the instant of launch.

Explanation / Answer

length of plastic stirreer, L = 0.06 m
charge on stirrer, Q = 10 nC
charge density of wire, lambda = 10^-7 C/m
initial distance d= 0.02 m

a. The strirrer is repelled as the +ve charge onthe long wire repels the +ve charge on the stirrer and hence applying an outward force that accelerated the stirrer away
b. Net force on the stirrer be F
   now consider a point at distance x form the wire, such that x > d and x < d + L , then x is on the stirrer
   consider an infinetismal thickness of the stirrer here dx
   charge on this part, dq = Q*dx/L
   Electric field due to the long wire at a point which is x m away from it, E = 2k*lambda/x
   so, Force on this small part dF = Edq = 2k*lambda*Qdx/x*L
   integratinf from x = d to x = d + l
   F = 2K*lambda*Q*ln(1 + l/x)/L
   putting in values
   F = 2*8.98*10^9*10^-7*10*10^-9 ln(1 + 0.06/0.02) / 0.06 = 4.149*10^-4 N

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