A point charge A has charge Q1. and mass M. At time t=0 point charge A is fired

Question

A point charge A has charge Q1. and mass M. At time t=0 point charge A is fired towards a stationary point charge B. and travels in a straight line towards the stationary charge. Point charge A starts out with speed v. Point charge B has charge Q2. The two charges initially have a very large separation so that the initial electric potential energy is zero. Charge Q1 comes to rest a distance X from Q2. Neglect any gravitational forces. Write the algebraic expression for the initial kinetic energy of Q1, when it has speed v. This gives you the initial total energy since the electric potential energy is 0. Write down the general algebraic expression for the electric potential energy of a pair of charges Q1 and Q2 separated by distance d. Denote the Coulomb constant by k. Your expression should be in terms of Q1. Q2. d and k Charge Q1 comes to rest a distance d=X from Q2. By equating the initial total energy from part A with the final potential energy at d=X, obtain an expression for the initial velocity. Your expression for v should be in terms of Q1, Q2. X, k and M. What conservation law did you use in part C? What is the initial speed required to reach a distance X=20 cm if Q1=3 nC, Q2=5 nC, and M= 0.6 milligrams. Coulomb constant k = 9 Times 10^9 N m^2/C^2

Explanation / Answer

part A:

initial kinetic energy of Q1=0.5*mass*speed^2

=0.5*M*v^2 J

part B:

electrical potential energy of two charges seprated by a distance d is given by

k*Q1*Q/d

where k=Coloumb constant

part c:

at distance X, electrical potential energy=k*Q*Q2/X

at this point, speed of Q1=0

==>final total energy of the system=k*Q1*Q2/X

applying energy conservation principle, total initial energy=total final energy

==>0.5*M*v^2=k*Q1*Q2/X

==>v=sqrt(2*k*Q1*Q2/(M*X))

part d:

energy conservation principle is being used in part C

part E:

given that X=0.2 m

Q1=3 nC

Q2=5 nC

M=0.6 mg

k=9*10^9

then initial speed, from the expression obtained in part c=

sqrt(2*9*10^9*3*10^(-9)*5*10^(-9)/(0.6*0.001*0.2))=0.0474 m/s

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