Three point charges are arranged along the xx-axis. Charge q1=+3.00q_1=+3.00 μ\muC is at the origin, and charge q2=−5.00q_2=-5.00 μ\muC is at x=0.200x = 0.200 m. Charge q2=−8.00q_2=-8.00 μ\muC. Where is q3q_3 located if the net force on q1q_1 is 7.007.00 N in the −x-x-direction?

Ch 21: Electric Charge and Electric Field

Young & Freedman Calc - University Physics 15th Edition

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Young & Freedman Calc 15th Edition

Ch 21: Electric Charge and Electric Field

Problem 16

Chapter 21, Problem 16

Three point charges are arranged along the $x$ -axis. Charge $q sub 1 equals positive 3.00$ $μ$ C is at the origin, and charge $q_{2} = - 5.00$ $μ$ C is at $x equals 0.200$ m. Charge $q_{2} = - 8.00$ $μ$ C. Where is $q sub 3$ located if the net force on $q sub 1$ is $7.00$ N in the $- x$ -direction?

Verified step by step guidance

Start by understanding that the net force on q1 is the vector sum of the forces exerted by q2 and q3. Since the net force is given as 7.00 N in the -x-direction, this means the force due to q3 must be greater than the force due to q2, and both must be in the -x-direction.

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

F = \frac{k q q}{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 q1 using the formula:

F = \frac{k 3.00 5.00}{{0.200}^{2}}

. This force will be in the -x-direction because q2 is negative.

Let the distance between q1 and q3 be

x

. The force exerted by q3 on q1 can be expressed as:

F = \frac{k 3.00 8.00}{x^{2}}

. This force will also be in the -x-direction because q3 is negative.

Set up the equation for the net force:

7.00 = \frac{k 3.00 8.00}{x^{2}}

\frac{k 3.00 5.00}{{0.200}^{2}}

. Solve for

x

to find the location of 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 direction of the force is along the line joining the charges, and it is attractive if the charges are opposite and repulsive if they are the same.

Superposition Principle

The superposition principle states that the net force on a charge due to multiple other charges is the vector sum of the individual forces exerted by each charge. This principle allows us to calculate the total force by considering each pair of charges separately and then adding the forces vectorially, taking into account their magnitudes and directions.

Vector Addition

Vector addition is a method used to combine multiple vectors, such as forces, into a single resultant vector. Each vector is represented by its magnitude and direction, and they are added by aligning them head-to-tail. The resultant vector is drawn from the tail of the first vector to the head of the last vector, providing both the magnitude and direction of the combined effect.

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Textbook Question

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