Two protons P and two positrons e+ are assembled at the corners of a square of s

Question

Two protons P and two positrons e+ are assembled at the corners of a square of side 1 m as shown below.

Each of these particles has a positive charge of q=+e, where e = 1.6022X10^19 C is the fundamental charge,

but the proton is much more massive: the mass of the proton is mP=1.6726X10^27 kg while the mass of the

positron equals the mass of the electron, me = 9.1094X10^31 kg

a) What total work is required to assemble these charges in the above conguration, by bringing the charges

in from innity?

b) If all of the particles are released from rest at time t=0, what are their nal speeds? [Hint: Use energy

conservation, and assume that the protons are so much more massive than the positrons that they remain

essentially stationary during the time it takes for the positrons to reach their nal speeds.]

Explanation / Answer

total work done is change in potential energy = 4*k*q^2 /d + 2*k*q^2 /(sqrt(2)*d) =1.2474 *10^(-21) J. final speed of positrons = sqrt (2*change in PE1/ m) = 37004.79 m/s. final speed of protons = sqrt (2*change in PE2/ m) = 524.88 m/s

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