Question

( 12. Two identical infinite positive line charges are
placed along the lines X = ta in the x-y plane. A
positive point charge placed at origin is restricted
to move along x-axis. Its equilibrium is
---
XX
-----
(1) Unstable
(2) Stable
(3) Neutral
(4) None of these
​

Answer 1

Answer:

Explanation:

First we must know the properties of the electric field:  

1) The electric field vector is tangent to the field lines at each point.

2) Electric field lines are open; they always leave positive or infinite charges and end in infinity or negative charges.

3) The number of lines leaving a positive charge or entering a negative charge is proportional to that charge.

4) The density of field lines at a point is proportional to the value of the electric field at that point.

5) Field lines cannot be cut. Otherwise there would be two different electric field vectors at the cut-off point.

6) At great distances from a load system, the lines are equally spaced and radial, the system behaving as a point load.

Effectively property number 6, we can reduce that will be neutral.

Answer 2

Answer:

The answer is option (2)

Its equilibrium is stable.

Explanation:

• There will be force  F₁ and F₂ acting in opposite direction
• There will be two line 1 and 2 having positive charges.
• q is the charge acting on the center. It has positive x-axis and negative x-axis
• The Force F₁ moves towards the positive x-axis and the force F₂ move towards the negative x-axis.

The force on q due to line 1  F₁= (λ q) ÷ 2πε₀a (towards positive x-axis)

The force on q due to line 2  F₂ = (λ q) ÷ 2πε₀a (towards negative x-axis)

Net force  F = F₁ - F₂

              F = 0

Therefore the net force is zero

If two identical infinite positive line charges are placed along the lines X= ta in the x-y plane. A positive point charge placed at origin is restricted to move along x-axis. Its equilibrium is stable.

Answer : Option (2)

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