Skip to main content
Ch 24: Gauss' Law
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 24: Gauss' LawProblem 4
Chapter 24, Problem 4

The electric field is constant over each face of the tetrahedron shown in FIGURE EX24.4. Does the box contain positive charge, negative charge, or no charge? Explain.
Tetrahedron with labeled electric field strengths: 20, 20, 15, and 10 N/C on its faces, illustrating Gauss' Law.

Verified step by step guidance
1
Understand the problem: The question is asking whether the tetrahedron contains positive charge, negative charge, or no charge. To determine this, we will use Gauss's law, which relates the electric flux through a closed surface to the charge enclosed within that surface.
Recall Gauss's law: Gauss's law states that the net electric flux (Φ) through a closed surface is proportional to the total charge (Q) enclosed within the surface. Mathematically, it is expressed as: ∮E⋅dA = Q/ε₀, where E is the electric field, dA is the infinitesimal area vector, and ε₀ is the permittivity of free space.
Analyze the electric field: The problem states that the electric field is constant over each face of the tetrahedron. This means that the electric flux through each face can be calculated as the product of the electric field magnitude and the area of the face, taking into account the direction of the field relative to the surface normal.
Calculate the net electric flux: To determine the net flux, sum the contributions of the electric flux through all four faces of the tetrahedron. If the net flux is zero, it implies no net charge is enclosed. If the net flux is positive, it indicates a positive charge is enclosed, and if negative, it indicates a negative charge is enclosed.
Interpret the result: Based on the net electric flux calculated in the previous step, conclude whether the tetrahedron contains positive charge, negative charge, or no charge. If the flux is zero, the box contains no charge. If the flux is nonzero, the sign of the flux will indicate the type of charge enclosed.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?

Key Concepts

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

Electric Field

An electric field is a region around a charged object where other charged objects experience a force. It is represented by field lines that indicate the direction and strength of the force. The electric field is defined as the force per unit charge, and its direction is taken to be the direction a positive test charge would move.
Recommended video:
Guided course
03:16
Intro to Electric Fields

Gauss's Law

Gauss's Law relates the electric flux through a closed surface to the charge enclosed by that surface. Mathematically, it states that the total electric flux is proportional to the enclosed charge. This principle is crucial for determining the presence of charge within a given volume, such as the tetrahedron in the question.
Recommended video:
Guided course
10:20
Gauss' Law

Charge Distribution

Charge distribution refers to how electric charge is spread out in a given space. It can be uniform or non-uniform, and it affects the electric field in that region. Understanding whether the charge is positive, negative, or neutral helps in analyzing the behavior of the electric field and the forces acting on charges within the tetrahedron.
Recommended video:
Guided course
04:03
Probability Distribution Graph
Related Practice
Textbook Question

The cube in FIGURE EX24.7 contains negative charge. The electric field is constant over each face of the cube. Does the missing electric field vector on the front face point in or out? What strength must this field exceed?

1
views
Textbook Question

FIGURE EX24.2 shows a cross section of two concentric spheres. The inner sphere has a negative charge. The outer sphere has a positive charge larger in magnitude than the charge on the inner sphere. Draw this figure on your paper, then draw electric field vectors showing the shape of the electric field.

1
views
Textbook Question

FIGURE EX24.1 shows two cross sections of two infinitely long coaxial cylinders. The inner cylinder has a positive charge, the outer cylinder has an equal negative charge. Draw this figure on your paper, then draw electric field vectors showing the shape of the electric field.

1
views
Textbook Question

The electric flux through the surface shown in FIGURE EX24.10 is 25 N m²/C. What is the electric field strength?

1
views
Textbook Question

A 2.0 cm × 3.0 cm rectangle lies in the xzxz-plane with unit vector n^\(\hat{n}\) pointing in the +y-direction. What is the electric flux through the rectangle if the electric field is E→=(4000i^−2000k^)\(\overrightarrow{E}\)=(4000\(\hat{i}\)-2000\(\hat{k}\)) N/C?

1
views
Textbook Question

FIGURE EX24.3 shows a cross section of two infinite parallel planes of charge. Draw this figure on your paper, then draw electric field vectors showing the shape of the electric field.

1
views