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Chapter 16: Q20Q (page 443)

Given two point charges, Q and 2Q, a distance \(l\) apart, is there a point along the straight line that passes through them where \(E = 0\) when their signs are (a) opposite, (b) the same? If yes, state roughly where this point will be.

Short Answer

Expert verified
  1. The point is near the charge Q in the opposite direction of the charge 2Q.
  2. The point is near the charge Q in the direction of the charge 2Q.

Step by step solution

01

Concepts

The electric field is a vector quantity.

The electric field is zero in a region, where the field due to two charges is opposite.

02

 Step 2: Explanation

Part (a)

Suppose the charges are opposite in signs. The electric fields due to the charges are in the same directions on the line joining the charges. The field is in the opposite direction outside the charges. As the Q charge is small, the point is near the charge Q in the opposite direction of the charge 2Q.

Part (b)

Suppose the charges are the same in sign. The electric fields due to the charges are in the opposite directions on the line joining the charges. Therefore the field is zero on the line joining the charges. As the Q charge is small, the point is near the charge Q in the direction of the charge 2Q.

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Most popular questions from this chapter

A point charge of mass 0.185 kg, and net charge\( + {\bf{0}}{\bf{.340 }}\mu {\bf{C}}\)hangs at rest at the end of an insulating cord above a large sheet of charge. The horizontal sheet of fixed uniform charge creates a uniform vertical electric field in the vicinity of the point charge. The tension in the cord is measured to be 5.18 N. Calculate the magnitude and direction of the electric field due to the sheet of charge (Fig. 16鈥�67).

FIGURE 16鈥�67 Problem 61.

(I) What is the repulsive electrical force between two protons\({\bf{4}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 15}}}}\;{\bf{m}}\)apart from each other in an atomic nucleus?

Question: (II) In Fig. 16鈥�62, two objects, \({{\bf{O}}_{\bf{1}}}\) and \({{\bf{O}}_{\bf{2}}}\) have charges \({\bf{ + 1}}{\bf{.0}}\;{\bf{\mu C}}\) and \({\bf{ - 2}}{\bf{.0}}\;{\bf{\mu C}}\), respectively, and a third object, \({{\bf{O}}_{\bf{3}}}\), is electrically neutral. (a) What is the electric flux through the surface \({A_1}\) that encloses all three objects? (b) What is the electric flux through the surface \({A_2}\) that encloses the third object only?

FIGURE 16鈥�62 Problem 39.

A water droplet of radius 0.018 mm remains stationary in the air. If the downward-directed electric field of the Earth is 150 N/C, how many excess electron charges must the water droplet have?

A negative point charge is in an electric field created by a positive point charge. Which of the following is true?

(a) The field points toward the positive charge, and the force on the negative charge is in the same direction as the field.

(b) The field points toward the positive charge, and the force on the negative charge is in the opposite direction to the field.

(c) The field points away from the positive charge, and the force on the negative charge is in the same direction as the field.

(d) The field points away from the positive charge, and the force on the negative charge is in the opposite direction to the field.
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