Ch 22: Electric Charges and Forces

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 22: Electric Charges and Forces

Problem 49b

Chapter 22, Problem 49b

A +2.0 nC charge is at the origin and a −4.0 nC charge is at x = 1.0 cm. Would the net force be zero for an electron placed at the same position? Explain.

Verified step by step guidance

Step 1: Begin by recalling Coulomb's Law, which describes the force between two charges. The formula is:

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

, where

k

is Coulomb's constant,

q

and

Q

are the charges, and

r

is the distance between them.

Step 2: Consider the electron placed at the same position as the −4.0 nC charge (x = 1.0 cm). The electron will experience forces due to both the +2.0 nC charge at the origin and the −4.0 nC charge at x = 1.0 cm.

Step 3: Analyze the direction of the forces. The electron has a negative charge, so it will be attracted to the positive +2.0 nC charge at the origin and repelled by the negative −4.0 nC charge at x = 1.0 cm. These forces act in opposite directions along the x-axis.

Step 4: Calculate the magnitudes of the forces using Coulomb's Law for each interaction. For the force due to the +2.0 nC charge, use the distance of 1.0 cm (converted to meters). For the force due to the −4.0 nC charge, the distance is effectively zero since the electron is at the same position as the −4.0 nC charge.

Step 5: Conclude that the net force cannot be zero because the force due to the −4.0 nC charge is undefined at zero distance (it approaches infinity), and the force due to the +2.0 nC charge is finite. Therefore, the electron would experience a net force and the system would not be in equilibrium.

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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 charged objects. It states that 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. This law is fundamental for calculating the forces acting on charges in an electric field.

Superposition Principle

The Superposition Principle in electrostatics states that the total force acting 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 analyze complex charge configurations by considering the effect of each charge separately before combining the results.

Electric Field

An electric field is a region around a charged object where other charges experience a force. The strength and direction of the electric field depend on the source charge and its position. For an electron placed in an electric field, the force it experiences will depend on the field's direction and magnitude, which can help determine if the net force on it is zero.

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Related Practice

Textbook Question

In a simple model of the hydrogen atom, the electron moves in a circular orbit of radius 0.053 nm around a stationary proton. How many revolutions per second does the electron make?

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Textbook Question

FIGURE P22.52 shows three charges and the net force on charge −q. Charge Q is some multiple α of q. What is α?

Textbook Question

What is the force F on the 1.0 nC charge at the bottom in FIGURE P22.47? Give your answer in component form.

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Textbook Question

You have two small, 2.0 g balls that have been given equal but opposite charges, but you don't know the magnitude of the charge. To find out, you place the balls distance apart on a slippery horizontal surface, release them, and use a motion detector to measure the initial acceleration of one of the balls toward the other. After repeating this for several different separation distances, your data are shown below. Use an appropriate graph of the data to determine the magnitude of the charge.

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Textbook Question

What is the force F on the 8.0 nC charge in FIGURE P22.44? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the +x-axis.

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Textbook Question

Objects A and B are both positively charged. Both have a mass of 100 g, but A has twice the charge of B. When A and B are placed 10 cm apart, B experiences an electric force of 0.45 N. What is the charge on A?