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Two positive charges A and B have charge +q and +2q, mass m and 2m. Both the charges are at rest when they are at distance x apart. Assume only force acting on either is the electrostatic force due to each other. Find: 1) Speed of charge A at instant separation b/w both charges is 2x. 2) Work done by electrostatic force on A while separation b/w charges change from x to 2x. 3) work done by electostatic force on A and B while separation b/w both charges changes from x to 2x.

Two positive charges A and B have charge +q and +2q, mass m and 2m. Both the charges are at rest when they are at distance x apart. Assume only force acting on either is the electrostatic force due to each other.
Find:
1) Speed of charge A at instant separation b/w both charges is 2x.
2) Work done by electrostatic force on A while separation b/w charges change from x to 2x.
3) work done by electostatic force on A and B while separation b/w both charges changes from x to 2x.

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2 Answers

vikas askiitian expert
509 Points
13 years ago

here only internal forces are responsible for motion ...no external force acts on the system so

momentam of system will remain conserved...

 

initail momentam = 0 = final momentam

let final velocities of m,2m are v1 , v2 then

mv1 + 2mv2 = 0

 v1 = -2v2          ....................1

 

now applying energy conservation

TE(total energy) = Kq.2q/x          (initial)

TE = kq.2q/2x + (1/2)mv12 + (1/2)2mv22           (final)

 

since energy is conserved so

(1/2)mv12 + (1/2)2mv22 + kq.2q/2x = kq.2q/x                 ....................2

 

from eq 1 substituting v1 in eq 2

2mv22 + mv22 = kqq/x

 v2 = [kq2/3x]1/2

v1 = 2[kq2/3x]1/2                                                   (ans1)

total change in KE = (1/2)mv12 + (1/2)2mv22 = work done                      (this is called work energy theorem)

from eq 2 , change in KE = kq2/x = net workdone on A,B                                    (ans3)

 

work done on A is change in KE of A = (1/2)mv12 = 2mkq2/3x                              (ans2)

 

approve if u like my ans

Priyansh Goel
21 Points
13 years ago

But why in finding out work done, we have not considered the electrostatic potential energy due to the other charge?

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