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Chapter 9: Problem 8

The below fields represent electric or magnetic fields associated with a long current-carrying wire, a single positive charge, two oppositely charged particles, two positive charges, and the field between two oppositely charged parallel sheets. (A) A, D, C, B, E (B) E, A, D, C, B (C) E, D, A, B, C (D) D, E, C, B, A (E) C, B, A, E, D

Short Answer

Expert verified
Answer: None of the given options match the fields correctly.

Step by step solution

01

Identifying the fields associated with each case.

Let's assign a letter to each of the given sources, and use that as a reference throughout the exercise: 1. Long current-carrying wire (L) 2. Single positive charge (S) 3. Two oppositely charged particles (O) 4. Two positive charges (P) 5. Field between two oppositely charged parallel sheets (F) Now, let's analyze the given options: (A) A, D, C, B, E (B) E, A, D, C, B (C) E, D, A, B, C (D) D, E, C, B, A (E) C, B, A, E, D
02

Finding the field associated with the long current-carrying wire.

Recall that the magnetic field around a long wire is circular, with concentric circles centered on the wire. Option A assumes that field A corresponds to the long wire. We can eliminate options B and C since they associate field E with the long wire, while a long-carrying wire doesn't produce straight lines. Option D assumes D corresponds to the long wire, which is incorrect as it's more radial than circular. Option E assumes C corresponds to the long wire with bi-directional arrows, which is not the case.
03

Finding the field associated with a single positive charge.

Option A assumes D is related to the single charge, which is incorrect because D shows two charges with opposite signs. Only options B and D associate A with a single charge. However, option D has eliminated in step 2.
04

Finding the field between two oppositely charged parallel sheets.

Option B assumes E is related to the field between two charged parallel sheets, which is correct because uniform straight lines represent the electric field between two oppositely charged parallel sheets.
05

Verifying the rest of Option B.

We have already verified E and A for option B. Now, we need to verify D, C, and B for the remaining fields: - (B) D refers to two oppositely charged particles (O): correct, as it has two charges with opposite signs and arrows pointing towards and away from them. - (B) C refers to two positive charges (P): correct, as it has two positive charges with arrows pointing away from them. - (B) B refers to a single positive charge (S): incorrect, as it has another charge responsible for the curve. In fact, A suits more accurately for a single positive charge. Since option B has errors, we conclude that none of the given options match the fields correctly.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Current-Carrying Wire
A current-carrying wire generates a magnetic field around itself. This magnetic field is not straight but rather forms circular patterns. Imagine the wire passing through the center of the circles, with the direction of the magnetic field determined by the right-hand rule. In this rule, if you point your thumb in the direction of the current, your curled fingers show the direction of the magnetic field. It forms concentric circles around the wire.

Key points about current-carrying wires include:
  • Magnetic fields generated are circular.
  • The strength of the magnetic field decreases as you move further from the wire.
  • The direction of the circles is determined by the current flow in the wire.
These concepts are crucial when considering the interaction between magnetic fields and other charges or particles nearby.
Charged Particles
Charged particles create electric fields around themselves. For a single positively charged particle, the electric field radiates outwards symmetrically, like rays from the sun. This field represents the force that a positive test charge would experience if placed in the vicinity of the charged particle: the test charge would be pushed away.

When two particles have opposite charges, their electric fields interact. This results in a pattern where lines emerge from the positive charge and converge into the negative charge. Key points about electric fields and charged particles include:
  • Electric fields can be radial (for single charges) or more complex (for multiple charges).
  • The direction of the field lines indicates whether a positively charged test particle would be attracted or repelled.
  • Strength of the field decreases with distance from the charge.
These principles help explain the forces and interactions charged particles have with each other and with external fields.
Parallel Sheets
A unique scenario arises when considering the electric field between two parallel sheets with opposite charges. This setup results in a uniform electric field. Between the sheets, field lines are straight, parallel, and evenly spaced, representing a consistent force experienced by a charge anywhere in the field region.

Important aspects of electric fields between parallel sheets include:
  • The uniformity of the field鈥攍ines do not curve but flow from positive to negative.
  • The field is constant in magnitude and direction.
  • This scenario is used to model many real-world applications, such as capacitors.
Understanding the behavior of electric fields between parallel sheets is essential in electronics and various engineering applications.

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Most popular questions from this chapter

Metal sphere \(A\) has a radius of \(5 \mathrm{~cm}\) and metal sphere \(B\) has a radius of \(10 \mathrm{~cm}\). Sphere \(A\) carries a charge of \(9 \mathrm{nC}\) and sphere \(B\) carries a charge of \(18 \mathrm{nC}\). If the surfaces of \(A\) and \(B\) are \(185 \mathrm{~cm}\) apart, the potential energy between them is (A) \(7.29 \times 10^{-17} \mathrm{~J}\) (B) \(7.88 \times 10^{-9} \mathrm{~J}\) (C) \(7.88 \times 10^{-7} \mathrm{~J}\) (D) \(7.29 \times 10^{-9} \mathrm{~J}\) (E) None of the above

A particle of mass \(m\) and charge \(+q\) is shot with velocity \(\mathbf{v}\) into a region of uniform magnetic field \(\mathbf{B}\). Suppose that \(\mathbf{v}\) points to the top of the page and \(\mathbf{B}\) points out of the page. Ignoring gravity, the particle (A) travels in a straight line. (B) moves clockwise in a circle with radius \(r=q B / m v\). (C) moves counterclockwise in a circle with radius \(r=q B / m v\). (D) moves clockwise in a circle with radius \(r=m v / q B\). (E) moves counterclockwise in a circle with radius \(r=m v / q B\).

An electron is released from rest just above a very large, negatively charged sheet, which carries surface charge density \(\sigma=5 \mathrm{nC} / \mathrm{m}^2\). When the electron is \(0.5 \mathrm{~m}\) above the sheet its speed is most nearly (A) \(4 \times 10^8 \mathrm{~m} / \mathrm{s}\) (B) \(3 \times 10^8 \mathrm{~m} / \mathrm{s}\) (C) \(5 \times 10^7 \mathrm{~m} / \mathrm{s}\) (D) \(1 \times 10^7 \mathrm{~m} / \mathrm{s}\) (E) \(300 \mathrm{~m} / \mathrm{s}\)

A solid copper sphere of radius \(R=10 \mathrm{~cm}\) carries a charge of \(+5 \mathrm{nC}\). a) Give an algebraic expression for the electric field at all distances \(r

The positively charged rod is brought near the large sphere, but without touching it. The two spheres are separated and lastly the rod removed to a distance. We can then say that (A) the big sphere will be positively charged and the smaller sphere will be negatively charged. (B) both spheres will be positively charged. (C) the big sphere will be negatively charged and the smaller sphere will be positively charged. (D) both spheres will be negatively charged. (E) all the charge will migrate to the smaller sphere.
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