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.

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Step 1: Begin by understanding the setup of the problem. You have two infinitely long coaxial cylinders: the inner cylinder is positively charged, and the outer cylinder is negatively charged. The charges are equal in magnitude but opposite in sign. This creates an electric field between the cylinders.

Step 2: Draw the figure on your paper. Represent the inner cylinder as a smaller circle and the outer cylinder as a larger concentric circle. Label the inner cylinder with a positive charge (+) and the outer cylinder with a negative charge (-).

Step 3: Recall that the electric field vectors point away from positive charges and toward negative charges. Between the cylinders, the electric field will point radially outward from the inner cylinder toward the outer cylinder.

Step 4: Draw electric field vectors between the cylinders. Start at the surface of the inner cylinder and draw arrows pointing radially outward toward the inner surface of the outer cylinder. Ensure the arrows are evenly spaced to represent the uniform field in this region.

Step 5: Note that outside the outer cylinder and inside the inner cylinder, the electric field is zero because the charges are equal and opposite, canceling each other out. You can label these regions as 'E = 0' to indicate no electric field exists there.

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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 electric field lines that indicate the direction and strength of the field. For a positive charge, the field lines radiate outward, while for a negative charge, they point inward. Understanding the configuration of charges helps in visualizing how the electric field behaves in different regions.

Gauss's Law

Gauss's Law relates the electric flux through a closed surface to the charge enclosed by that surface. It states that the total electric flux is proportional to the enclosed charge, allowing for the calculation of electric fields in symmetrical charge distributions. This principle is particularly useful for coaxial cylinders, as it simplifies the analysis of the electric field between and outside the cylinders.

Superposition Principle

The superposition principle states that the total electric field created by multiple charges is the vector sum of the electric fields produced by each charge individually. This principle is essential when dealing with systems like coaxial cylinders, as it allows for the determination of the resultant electric field by considering the contributions from both the inner and outer charged cylinders.