Question

Two charged objects 1 and 2 are held at a distance r apart. Object 1 has mass m and charge +3q, and object 2 has mass 2m and charge +q. The objects are released from rest. Assume that the only force exerted on either object is the electric force exerted by the other object.

Part B

When the objects are at a distance 4r apart, what is the speed of object 1?

Part C

When the objects are at a distance 4r apart, what is the speed of object 2?

Part D

When the objects are very far apart, what is the speed of object 1?

Part E

When the objects are very far apart, what is the speed of object 2?

Answer 1

Mass of 1st object,

Charge of 1st object,

Mass of 2nd object,

Charge of 2nd object,

Initial distance between charges= r

Then initial total energy of the system will be only the total electrostatic potential energy since initially the system was at rest.

Thus we can write,

...........................(1)

B). Now when they start moving and are 4r distance apart. Let speed of 1st charge be v₁ and that of 2nd object be v₂. Then using Momentum conservation principle:

  

  

  

  ...................................(2)

Then we can write total energy of the system as

  

Using equation 2 in above,

........................(3)

Then using Energy conservation Principle,

  (ANS)

C). Using equation (2),

  

(ANS)