Have you worked through the online tutorial on electric potential energy and pot

Question

Have you worked through the online tutorial on electric potential energy and potential difference? Yes____ No _____ Possibly useful information: F = k|q_1|q_2|/r^2: W = -Delta U = k q_1q_2/r: K = 1/2 mv^2: Phi = Q_enc/epsilon_0 = contourintegral E^vector middot dA^vector: V_sphere = 4/3 pi r^3 F = ma: F = qE: E = V/d: A^vector middot B^vector = |A||B| cos alpha Suppose that two protons (of mass m_p each) are released from rest when they are a distance d apart. Calculate their speed v, symbolically in terms of given quantities, when they are 4d apart.

Explanation / Answer

let initial velocity of protons (u)=0m/s

when the two protons are separated by d apart

initial energy=(1/4pie0)(q^2/d)

here q=charge of each proton

d=initial separation

e0=permitivity of free space

since both the charged particle are protons they have equal velocities when they are 4d apart

m=mass of proton

final energy=electric potential energy+kinetic energy

=(1/4pie0)(q^2/4d)+(1/2)mv^2+(1/2)mv^2

according to law of conservation of energy

initial energy=final energy

(1/4pie0)(q^2/d)=(1/4pie0)(q^2/4d)+MV^2

on simplifying we get

v=(3q^2/16pie0m)^(1/2)

the velocity of each proton is v=(3q^2/16pie0m)^(1/2) when they are 4d apart

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