Two electrons, each with mass m and charge q, are released from positions very far from each other. With respect to a certain reference frame, electron A has initial nonzero speed v toward electron B in the positive x-direction, and electron B has initial speed 3v toward electron A in the negative x-direction. The electrons move directly toward each other along the x-axis (very hard to do with real electrons). As the electrons approach each other, they slow due to their electric repulsion. This repulsion eventually pushes them away from each other. Which of the following statements about the motion of the electrons in the given reference frame will be true at the instant the two electrons reach their minimum separation?

a. Electron A is moving faster than electron B.
b. Electron B is moving faster than electron A.
c. Both electrons are moving at the same (nonzero) speed in the opposite direction.
d. Both electrons are moving at the same (nonzero) speed in the same direction.
e. Both electrons are momentarily stationary.

the minimum separation is achived when the relative speed between the electrons is 0, so, the variation of this relative speed is 4v, 2v in each electron speed. The electron A will have a speed of v (v-2v=-v) in the same direction of the electron B speed, the magnitud of the latter will be |4v-2v|= 2v

ConcepcionPetillo ConcepcionPetillo · Answer 2 · 2022-02-22T18:16:00+01:00

The correct option is (d)

The problem can be treated as a perfectly inelastic collision so both electrons are moving at the same (nonzero) speed in the same direction.

Conservation of momentum:

The electric force acting on both the electrons will be same, so the acceleration acting on the electrons will also be the same.

Minimum separation will be achieved when both the electron come closest to each other, but due to repulsion, they will not collide.

Now if we apply the concept of conservation of momentum then the initial momentum must be equal to the final momentum at the instant they are at the minimum separation.

If we take right as positive direction and left as negative direction and the mass of the electron be m then,

initial momentum = mv - 3mv = -2mv or 2mv to the left = final momentum

Now the instant at which the minimum separation is achieved can be treated as a perfectly inelastic collision and both the electrons will move towards left together with the same velocity maintaining a constant distance for a while.

Learn more about inelastic collision:

https://brainly.com/question/26262983?referrer=searchResults