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Chapter 16: Problem 38

Sketch the electric field lines near two isolated and equal (a) positive point charges and (b) negative point charges. Include arrowheads to show the field directions.

Short Answer

Expert verified
Question: Sketch the electric field lines near two isolated equal point charges for both positive and negative charges. Discuss the properties of electric field lines and how they apply to the drawings. Answer: Electric field lines represent the direction of electric force experienced by a positive test charge placed at a point in the field. Some key properties of electric field lines include: 1. Originating from positive charges and terminating at negative charges or infinity. 2. Never intersecting each other. When sketching electric field lines for equal positive point charges, the lines will originate from the charges and fan out away from them without intersecting. For equal negative point charges, the electric field lines will start from infinity and bend towards the charges, connecting both charges in a smooth curvature with no intersections. In both cases, the density of lines indicates the strength of the electric field.

Step by step solution

01

(Understanding electric field lines)

Electric field lines represent the direction of the electric force experienced by a positive test charge placed at a point in the field. The density of lines in a region indicates the strength of the electric field. Some properties of electric field lines are: 1. Electric field lines always begin on positive charges and end on negative charges or at infinity. 2. Electric field lines never intersect each other. 3. The electric field strength at a point can be determined by the tangent drawn to the field line at that point.
02

(Sketching electric field lines for equal positive point charges)

As we have two equal positive point charges, the electric field lines will originate from these charges. Sketch the charges on a plane, placed at some distance from each other. Then, draw electric field lines that start from one charge and move away from it, bending around the other charge in a way that they never intersect and maintain a smooth curvature. Repeat this for both charges. Also, include some electric field lines that go to infinity. Add arrowheads on the field lines to show the direction. The resulting sketch should show the electric field lines fanning out from the positive charges and never intersecting.
03

(Sketching electric field lines for equal negative point charges)

Now, let's consider the case of two equal negative point charges. In this case, the electric field lines will terminate at the charges. First, sketch the charges on a plane, placed at some distance from each other. Draw electric field lines that start from infinity and bend towards the charges, approaching them in a smooth curvature. Some of these field lines should connect both charges, originating from infinity, moving toward the first charge, bending around, and terminating at the second charge. Add arrowheads on the field lines to show the direction. The resulting sketch should show the electric field lines converging toward the negative charges and never intersecting.

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Most popular questions from this chapter

A parallel-plate capacitor consists of two flat metal plates of area \(A\) separated by a small distance \(d\). The plates are given equal and opposite net charges \(\pm q\) (a) Sketch the field lines and use your sketch to explain why almost all of the charge is on the inner surfaces of the plates. (b) Use Gauss's law to show that the electric field between the plates and away from the edges is $E=q /\left(\epsilon_{0} A\right)=\sigma / \epsilon_{0} \cdot(\mathrm{c})$ Does this agree with or contra- dict the result of Problem \(70 ?\) Explain. (d) Use the principle of superposition and the result of Problem 69 to arrive at this same answer. [Hint: The inner surfaces of the two plates are thin, flat sheets of charge.]
In lab tests it was found that rats can detect electric fields of about $5.0 \mathrm{kN} / \mathrm{C}\( or more. If a point charge of \)1.0 \mu \mathrm{C}$ is sitting in a maze, how close must the rat come to the charge in order to detect it?
Positive point charges \(q\) and \(2 q\) are located at \(x=0\) and \(x=3 d,\) respectively. What is the electric field at \(x=2 d\) (point \(S\) )?
A flat conducting sheet of area \(A\) has a charge \(q\) on each surface. (a) What is the electric field inside the sheet? (b) Use Gauss's law to show that the electric field just outside the sheet is \(E=q /\left(\epsilon_{0} A\right)=\sigma / \epsilon_{0} .\) (c) Does this contradict the result of Problem \(69 ?\) Compare the field line diagrams for the two situations.
A metallic sphere has a charge of \(+4.0 \mathrm{nC} .\) A negatively charged rod has a charge of \(-6.0 \mathrm{nC} .\) When the rod touches the sphere, $8.2 \times 10^{9}$ electrons are transferred. What are the charges of the sphere and the rod now?
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