Three point charges are arranged on a line. Charge q3=+5.00q_3=+5.00 nC and is at the origin. Charge q2=−3.00q_2=-3.00 nC and is at x=+4.00x = +4.00 cm. Charge q1q_1 is at x=+2.00x = +2.00 cm. What is q1q_1 (magnitude and sign) if the net force on q3q_3 is zero?

Ch 21: Electric Charge and Electric Field

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 21: Electric Charge and Electric Field

Problem 13

Chapter 21, Problem 13

Three point charges are arranged on a line. Charge $q sub 3 equals positive 5.00$ nC and is at the origin. Charge $q_{2} = - 3.00$ nC and is at $x equals positive 4.00$ cm. Charge $q sub 1$ is at $x equals positive 2.00$ cm. What is $q sub 1$ (magnitude and sign) if the net force on $q sub 3$ is zero?

Verified step by step guidance

Understand that the net force on q3 is zero, meaning the forces exerted by q1 and q2 on q3 must be equal in magnitude but opposite in direction.

Use Coulomb's Law to express the force between two point charges:

F = \frac{k q q r r}{r^{2}}

, where

k

is Coulomb's constant,

q

are the charges, and

r

is the distance between them.

Calculate the force exerted by q2 on q3 using the formula:

F = \frac{k 3.00 5.00 10 {-9}^{2}}{{0.04}^{2}}

Set up the equation for the force exerted by q1 on q3 to be equal in magnitude to the force exerted by q2 on q3:

\frac{k q 5.00 10 {-9}^{2}}{{0.02}^{2}} = \frac{k 3.00 5.00 10 {-9}^{2}}{{0.04}^{2}}

Solve for q1, ensuring that the sign of q1 is such that the direction of the force it exerts on q3 is opposite to the force exerted by q2 on q3.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Coulomb's Law

Coulomb's Law describes the electrostatic force between two point charges. The force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The force is attractive if the charges are of opposite signs and repulsive if they are of the same sign.

Superposition Principle

The superposition principle states that the net force on a charge is the vector sum of all individual forces acting on it. In this problem, the net force on charge q3 is the sum of the forces due to q1 and q2. For the net force to be zero, these forces must be equal in magnitude and opposite in direction.

Equilibrium of Forces

Equilibrium occurs when the net force acting on an object is zero, resulting in no acceleration. In the context of electrostatics, this means that the forces due to surrounding charges must balance each other out. For q3 to be in equilibrium, the forces exerted by q1 and q2 must cancel each other out, allowing us to solve for the unknown charge q1.

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(b) What gravitational force would each box of protons exert on the other box?

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