The Net Force on a Test Charge at Equilibrium Due to Two Point Charges

In summary, two charges, one positive and one negative, are placed on the x-axis at the origin and x=0.600m respectively. The net force on a small test charge +q will be zero when it is located at a distance of 0.6m from the negative charge, on the negative x-axis. Equating the forces exerted by the two charges yields the equation kq1q2/(r)^2 = kq1q2/(r+6)^2, where q1 represents the test charge and q2 represents the magnitude of the two charges. Cancelling out the charges and solving for r gives the position on the x-axis where the net force on the test charge would be zero.
  • #1
Larrytsai
228
0

Homework Statement


Two charges, one of 2.50 micro coulomb, and the other of -3.50 micro coulomb, are placed on the x-axis, one at the origin and the other at x=0.600m, as shown in Fig 21.36. Find the position on the x-axis where the net force on a small charge +q would be zero


Homework Equations


F= kq1q1/r^2


The Attempt at a Solution


I tried to equate the force when the distance of the two charges are 0.6m away to the force when the distance is x+0.6
 
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  • #2
You can imagine that the charge has to be on the negative x-axis for the force exerted by the positive charge to equal the force exerted by the negative charge. Assume that it's a distance "d" from the origin; then it would be d+0.6 m from the other charge. Proceed from there.
 
  • #3
yeah i have made that assumption by equating F1=F2, but, i don't understand what's happening after, i cancel my constants, and my charges should cancel so i end up with 1/(0.6)^2 = 1/(x+0.6)^2 , and u end up with 0
 
  • #4
How do the charges cancel? One's 3.5 mC (in magnitude) and the other's 2.5 mC.
 
  • #5
well i have F1=F2 so its kq1q2/(r)^2 = kq1q2/(r+6)^2
 
  • #6
Don't apply equations without any thought. Think about what the letters in this equation:

kq1q2/(r)^2 = kq1q2/(r+6)^2

stand for. Assuming q1 is the test charge, do the q2's represent the same charge?
 
  • #7
ideasrule said:
Don't apply equations without any thought. Think about what the letters in this equation:

kq1q2/(r)^2 = kq1q2/(r+6)^2

stand for. Assuming q1 is the test charge, do the q2's represent the same charge?

im sorry but i do not understand the last part, if we assume q1 is the test charge, so we are able to cancel q1 out?
 

1. What is Coulomb's Law?

Coulomb's Law is a physical law that describes the electrostatic interaction between electrically charged particles. It states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

2. How does distance affect the force between charged particles?

The force between charged particles decreases as the distance between them increases. This is because the inverse square relationship in Coulomb's Law means that the force decreases exponentially as the distance increases.

3. Can Coulomb's Law be applied to all charged particles?

Yes, Coulomb's Law can be applied to all charged particles, as long as they are at rest relative to each other and the distance between them is large enough to neglect any quantum effects.

4. What is the unit of force in Coulomb's Law?

The unit of force in Coulomb's Law is the Newton (N). This is because the force is given by the product of the two charges (measured in Coulombs) divided by the square of the distance (measured in meters squared).

5. How does Coulomb's Law relate to the concept of electric fields?

Coulomb's Law is the mathematical expression of the relationship between electric charges and the force they exert on each other. Electric fields, on the other hand, describe the influence of these charges on the space around them. The strength of an electric field at a certain point is directly proportional to the force that a charged particle would experience at that point.

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