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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

\(\mathrm{A}+2.0\) -nC point charge is \(3.0 \mathrm{cm}\) away from a $-3.0 \mathrm{-nC}$ point charge. (a) What are the magnitude and direction of the electric force acting on the +2.0 -nC charge? (b) What are the magnitude and direction of the electric force acting on the -3.0 -nC charge?
A point charge \(q_{1}=+5.0 \mu \mathrm{C}\) is fixed in place at \(x=0\) and a point charge \(q_{2}=-3.0 \mu \mathrm{C}\) is fixed at \(x=\) $-20.0 \mathrm{cm} .\( Where can we place a point charge \)q_{3}=-8.0 \mu \mathrm{C}$ so that the net electric force on \(q_{1}\) due to \(q_{2}\) and \(q_{3}\) is zero?
What are the magnitude and direction of the acceleration of a proton at a point where the electric field has magnitude \(33 \mathrm{kN} / \mathrm{C}\) and is directed straight up?
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 thin, flat sheet of charge has a uniform surface charge density \(\sigma(\sigma / 2\) on each side). (a) Sketch the field lines due to the sheet. (b) Sketch the field lines for an infinitely large sheet with the same charge density. (c) For the infinite sheet, how does the field strength depend on the distance from the sheet? [Hint: Refer to your field line sketch.J (d) For points close to the finite sheet and far from its edges, can the sheet be approximated by an infinitely large sheet? [Hint: Again, refer to the field line sketches.] (e) Use Gauss's law to show that the magnitude of the electric field near a sheet of uniform charge density \(\sigma\) is $E=\sigma /\left(2 \epsilon_{0}\right)$
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