A charge +Q is fixed. Another charge +2q and mass M is projected

In summary, the problem involves a fixed charge +Q and a projected charge +2q with mass M at a distance R from the fixed charge. The charge is projected at an angle of 30 degrees with a velocity of v, and the task is to find the minimum separation between the two charges when the velocity becomes 1/√3 times the original velocity. To solve this, the equation F= (k2Qq) / (R^2) is used, assuming gravity is absent. However, since it is a conservation of energy question, V(r) should also be taken into consideration. Additionally, the angular momentum around the fixed charge must also be conserved. After solving, the minimum separation between the two charges
  • #1
Asphyx820
10
0

Homework Statement



A charge +Q is fixed. Another charge +2q and mass M is projected from a distance R from the fixed charge at and angle 30 with the horizontal towards the fixed charge (like a projectile) at a speed of v
Find the minimum separation between the two charges if the velocity becomes 1/√3 times of the projected velocity at this moment (assume gravity to be absent)

Homework Equations



1) F= (k2Qq) / (R^2) where (k=1/4∏ε)

The Attempt at a Solution



Since the gravity is absent, should I use acceleration of the +2q charge instead of gravity (which can be found out from (1) as mass of +2q is M)
I have tried this method but somewhere I'm getting wrong as I cannot reach the answer
pls help me as I have been trying this from past 2 days.
the correct answer is (√3/2)R
 
Physics news on Phys.org
  • #2


This is worded as an Energy Conservation question, so use V(r) ... but you also need to conserve angular momentum around the fixed charge (M v1 R1 sin 150 = M v2 R2).
 
  • #3


Ok.. so is this the way ?
M (√3/2)v R1 (1/2) = M (v/2) R2
therefore , R2 = (√3/2)R1
(so what is the use of energy conservation?)

and I was thinking about the path of +2q charge. It would be repelled by the +Q charge, so it shouldn't move towards the +Q charge. So how will the path of +2q charge be?? away from it or something else?
 
Last edited:

FAQ: A charge +Q is fixed. Another charge +2q and mass M is projected

What is the force acting on the charge +2q when it is projected towards the fixed charge +Q?

The force acting on the charge +2q is given by Coulomb's law, which states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

How does the mass of the projected charge +2q affect the force between it and the fixed charge +Q?

The mass of the projected charge +2q does not directly affect the force between the two charges. However, the mass does affect the acceleration of the charge, which in turn affects the force through Newton's second law (F=ma).

Why does the fixed charge +Q not move when the charge +2q is projected towards it?

The fixed charge +Q does not move because it is fixed in place. In other words, it is held in place by some external force or constraint and is unable to move.

Can the charge +2q and the fixed charge +Q have the same sign and still experience a force?

Yes, the charges can have the same sign (+ or -) and still experience a force. In this case, the force would be repulsive, meaning the charges would push away from each other.

How does the distance between the two charges affect the force between them?

The force between the two charges is inversely proportional to the square of the distance between them. This means that as the distance between the charges increases, the force decreases and vice versa. This relationship is described by Coulomb's law.

Back
Top