Learning Goal: To practice Problem-Solving Strategy 25.1 for electric force prob

Question

Learning Goal:

To practice Problem-Solving Strategy 25.1 for electric force problems.

Two charged particles, with charges q1=q and q2=4q, are located at a distance d=2.00cm  apart on the x axis. A third charged particle, with charge q3=q, is placed on the x axis such that the magnitude of the force that charge 1 exerts on charge 3 is equal to the force that charge 2 exerts on charge 3.

Find the position of charge 3 when q = 2.00nC .

PROBLEM-SOLVING STRATEGY 25.1 Electric forces and Coulomb's law

MODEL: Identify point charges or objects that can be modeled as point charges.

VISUALIZE: Use a pictorial representation to establish a coordinate system, show the positions of the charges, show the force vectors on the charges, define distances and angles, and identify what the problem is trying to find. This is the process of translating words to symbols.

SOLVE: The mathematical representation is based on Coulomb

Explanation / Answer

Let r1 be the distance of charge q3 from q1, the distance of q2 is r2

The force onq3 by q is k q^2 / r1^2
and by q2 is k4q^2/ r2^2

Equating the two
k q^2 / r1^2 = k4q^2/ r2^2
[r2/ r1]^2 = 4
r2/ r1 = 2 or -2
r2 = 2r1 or r2 = -2r1

But r1 + r2 = 2
Using r2 = 2r1
3r1 = 2
r1 = 2/3 = 0.66 m
and r1 = 1.33m
====================
Using r2 = - 2r1

r1 -2r1 = 2
r1 = -2 m
and r2 =-2{-2} = 4 m
===========================

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.