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Chapter 16: Q19Q (page 443)

Show, using the three rules for field lines given in Section 16鈥�8, that the electric field lines starting or ending on a single point charge must be symmetrically spaced around the charge.

Short Answer

Expert verified

The electric field at the same distance has the same magnitude for a specific charge. Therefore the density of the field lines is the same at the same distance from the charge.

Step by step solution

01

Concepts

The electric field lines are an imaginary path for a test charge to move.

The direction of the electric field lines shows the direction of the electric field at any location.

02

Explanation

The three rules are:

  1. The electric field lines indicate the direction of the electric field at any point on the field line.
  2. The density of field lines is proportional to the magnitude of the electric field at any location.
  3. Electric field lines start on positive charges and end on negative charges.

You know the electric field at the same distance has the same magnitude for a specific charge. Therefore the density of the field lines is the same at the same distance from the charge. Hence, the electric field lines are symmetrically spaced around the charge.

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Most popular questions from this chapter

Fred the lightning bug has a mass m and a charge \( + q\) Jane, his lightning-bug wife, has a mass of \(\frac{3}{4}m\) and a charge \( - 2q\). Because they have charges of opposite sign, they are attracted to each other. Which is attracted more to the other, and by how much?

(a) Fred, twice as much.

(b) Jane, twice as much.

(c) Fred, four times as much.

(d) Jane, four times as much.

(e) They are attracted to each other by the same amount.

\({Q_1} = - {\bf{0}}{\bf{.10}}\;{\bf{\mu C}}\)is located at the origin. \({Q_2} = {\bf{ + 0}}{\bf{.10}}\;{\bf{\mu C}}\) is located on the positive x-axis at \(x{\bf{ = 1}}{\bf{.0}}\;{\bf{m}}\). Which of the following is true of the force on \({Q_1}\) due to \({Q_2}\)?

(a) It is attractive and directed in the \( + x\) direction.

(b) It is attractive and directed in the \( - x\) direction.

(c) It is repulsive and directed in the \( + x\) direction.

(d) It is repulsive and directed in the \( - x\) direction.

Why does a shirt or blouse taken from a clothes dryer sometimes cling to your body?

Packing material made of pieces of foamed polystyrene can easily become charged and stick to each other. Given that the density of this material is about \({\bf{35 kg/}}{{\bf{m}}^{\bf{3}}}\), estimate how much charge might be on a 2.0-cm-diameter foamed polystyrene sphere, assuming the electric force between two spheres stuck together is equal to the weight of one sphere.

(III) Two small nonconducting spheres have a total charge of \({\bf{90}}{\bf{.0}}\;{\bf{\mu C}}\). (a) When placed 28.0 cm apart, the force each exerts on the other is 12.0 N and is repulsive. What is the charge on each? (b) What if the force were attractive?
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