Question

An electron is projected toward a fixed position charge particle having a non-zero angle of projection then

• A. Linear momentum remains conserve
• B. Angular momentum conserve
• C. Torque of electric force is non zero
• D. Energy of system is variable

Answer 1

Answer: (B)

Angular momentum is conserved.

Answer 2

The problem describes an electron projected towards a fixed positive charge particle with a non-zero angle of projection. We need to analyze the conservation laws for this system.

Let's consider the system as the electron and the fixed positive charge.

1. Linear momentum conservation:

   • The positive charge particle is "fixed". This implies that an external force is acting on it to keep it stationary.
   • This external force acts on the system (electron + fixed charge).
   • Since there is a net external force acting on the system, the total linear momentum of the system is not conserved.
   • Therefore, statement 1 is incorrect.

2. Angular momentum conservation:

   • The electric force between the electron and the fixed positive charge is a central force. This means the force always acts along the line connecting the two particles.
   • If we choose the fixed positive charge as the origin (reference point), the position vector $\vec{r}$ of the electron from the origin and the electric force $\vec{F}$ on the electron are collinear (parallel or anti-parallel).
   • The torque $\vec{\tau}$ of the electric force about the fixed positive charge is given by $\vec{\tau} = \vec{r} \times \vec{F}$.
   • Since $\vec{r}$ and $\vec{F}$ are collinear, their cross product is zero ($\vec{\tau} = 0$).
   • As the net torque on the electron about the fixed positive charge is zero, its angular momentum about this point is conserved.
   • Therefore, statement 2 is correct.

3. Torque of electric force is non-zero:

   • As explained in point 2, the electric force is a central force, and its torque about the center of force (the fixed positive charge) is zero.
   • Therefore, statement 3 is incorrect.

4. Energy of system is variable:

   • The electric force is a conservative force.
   • The external force holding the positive charge fixed does no work, because the point of application of this force does not move (displacement is zero).
   • Since the only force doing work is the conservative electric force (internal to the system), and no external non-conservative forces do work, the total mechanical energy (kinetic + potential) of the system (electron + fixed positive charge) is conserved.
   • Therefore, statement 4 is incorrect.

Based on the analysis, only statement 2 is correct.