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A thin circular sheet of glass of diameter 3 m is rubbed with a cloth on one surface and becomes charged uniformly. A chloride ion (a chlorine atom that has gained one extra electron) passes near the glass sheet. When the chloride ion is near the center of the sheet, at a location 0.8 mm from the sheet, it experiences an electric force of 5 × 10−15 N, toward the glass sheet. It will be useful to you to draw a diagram on paper, showing field vectors, force vectors, and charges, before answering the following questions about this situation. Which of the following statements about this situation are correct? Select all that apply. (1) The electric field that acts on the chloride ion is due to the charge on the glass sheet and to the charge on the chloride ion. (2) The electric field of the glass sheet is equal to the electric field of the chloride ion. (3) The charged disk is the source of the electric field that causes the force on the chloride ion. (4) The net electric field at the location of the chloride ion is zero. (5) The force on the chloride ion is equal to the electric field of the glass sheet. In addition to an exact equation for the electric field of a disk, the text derives two approximate equations. In the current situation we want an answer that is correct to three significant figures. Which of the following is correct? We should not use an approximation if we have enough information to do an exact calculation. (1) R≫z, so it is adequate to use the most approximate equation here. (2) z is nearly equal to R, so we have to use the exact equation. (3) z≪R, so we can’t use an approximation. How much charge is on the surface of the glass disk? Give the amount, including sign and correct units

Short Answer

Expert verified

Option (3) is correct and the charge on the surface of glass disk is3.9×10-6C .

Step by step solution

01

Identification of given data

The given data can be listed below,

  • The diameter of circular glass disk is,R=3m
  • The radial distance of point from center of disk is,z=0.8mm0.8×10-3m
  • The force experienced by glass sheet is,F=5×10-5N/C
02

Concept/Significance of electrostatic force

When an electric charge in a certain reference frame is stationary. Then the term "electrostatic field" or "force" is appropriate. Both electrostatic and magnetic fields and forces are present when a charge is moving.

03

Determination of the true statement.

The claims in the problem:

  1. The electric field that acts on the ion is caused only by the charge on the disk, so this statement is false. The force is caused by both charged because if the ion were neutral, it would not feel a force.
  2. Due to Newton's third law, the force exerted on the ion by the charged disk is the same as the force exerted on the disk by the ion. Since their charges are different (we calculate this later), the electric fields have to be different, so this statement is false.
  3. This statement is true as the chloride ion has a charge and since all other charges cancel, the chloride ion effectively acts like just one electron in the presence of an external field. The ion feels a force because of the charged disk and the force is

Here, e is the charge on the ion and E is the electric field.

  1. Since the force on the ion is non-zero, the field at the position of the ion cannot be zero, so this statement is false.
  2. The force on the ion is equal to the electric field times the charge of the ion, so this statement is false.
04

Step 4: Determination of charge is on the surface of the glass disk

The approximate electric field on the surface of disk,

E=Q/A2ε0

Rearrange the above equation,

F=eE=eQ/A2ε0Q=2εAFe

Substitute all the values in the above,

Q=28.85×10-12C2/Nm21.5m2π5×10-15N1.6×10-19C=3.9×10-6C

Thus, the force is attractive the charge on ion negative so the charge on disk must be positive with value3.9×10-6C .

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Most popular questions from this chapter

Suppose that the radius of a disk is 21 cm, and the total charge distributed uniformly all over the disk is 5×10-6C. (a) Use the exact result to calculate the electric field 1 mm from the center of the disk. (b) Use the exact result to calculate the electric field 3 mm from the center of the disk. (c) Does the field decrease significantly?

You stand at location A, a distance d from the origin, and hold a small charged ball. You find that the electric force on the ball is 0.08 N. You move to location B, a distance 2d from the origin, and find the electric force on the ball to be 0.04 N. What object located at the origin might be the source of the field? (1) A point charge, (2) A dipole, (3) A uniformly charged rod, (4) A uniformly charged ring, (5) A uniformly charged disk, (6) A capacitor, (7) A uniformly charged hollow sphere, (8) None of the above If the force at B were 0.0799 N, what would be your answer? If the force at B were 0.01 N, what would be your answer? If the force at B were 0.02 N, what would be your answer?

The rod in Figure 15.49 carries a uniformly distributed positive charge. Which arrow (a–h) best represents the direction of the electric field at the observation location marked with a red X?

Two rings of radius 2 cm are 20 cm apart and concentric with a common horizontal x axis. What is the magnitude of the electric field midway between the rings if both rings carry a charge of +35 nC?

A thin glass rod of length 80 cmis rubbed all over with wool and acquires a charge of 60 nC, distributed uniformly over its surface. Calculate the magnitude of the electric field due to the rod at a location 7 cmfrom the midpoint of the rod. Do the calculation two ways, first using the exact equation for a rod of any length, and second using the approximate equation for a long rod.

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