Worksheet: Using Ampere’s Law to Calculate the Magnetic Field of Currents

In this worksheet, we will practice using Ampere’s law to relate the current through a closed conducting path to the magnetic field produced by that current.

Q1:

The coil whose lengthwise cross section is shown in the accompanying figure carries a current 𝐼 and has 𝑁 evenly spaced turns distributed along the length 𝑙.

Evaluate ο…‡β‹…BId in terms of πœ‡οŠ¦ and 𝐼 for path 𝐴.

  • A0
  • Bβˆ’1.3πœ‡πΌοŠ¦
  • C1.3πœ‡πΌοŠ¦
  • D3πœ‡πΌοŠ¦
  • E1.7πœ‡πΌοŠ¦

Evaluate ο…‡β‹…BId in terms of πœ‡οŠ¦ and 𝐼 for path 𝐡.

Evaluate ο…‡β‹…BId in terms of πœ‡οŠ¦ and 𝐼 for path 𝐢.

  • A0
  • Bβˆ’5πœ‡πΌοŠ¦
  • C2.6πœ‡πΌοŠ¦
  • D3.5πœ‡πΌοŠ¦
  • E7πœ‡πΌοŠ¦

Evaluate ο…‡β‹…BId in terms of πœ‡οŠ¦ and 𝐼 for path 𝐷.

  • A0
  • Bβˆ’πœ‡πΌοŠ¦
  • Cβˆ’2πœ‡πΌοŠ¦
  • D2πœ‡πΌοŠ¦
  • Eπœ‡πΌοŠ¦

Q2:

The following figure shows a rectangular current loop that carries a current 𝐼.

Evaluate ο…‡β‹…BId in terms of πœ‡οŠ¦ and 𝐼 for path 𝐴.

  • Aβˆ’πœ‡πΌοŠ¦
  • Bπœ‡πΌοŠ¦
  • C1.5πœ‡πΌοŠ¦
  • Dβˆ’1.5πœ‡πΌοŠ¦
  • E0

Evaluate ο…‡β‹…BId in terms of πœ‡οŠ¦ and 𝐼 for path 𝐡.

Evaluate ο…‡β‹…BId in terms of πœ‡οŠ¦ and 𝐼 for path 𝐢.

  • Aπœ‡πΌοŠ¦
  • B0
  • Cβˆ’πœ‡πΌοŠ¦
  • Dβˆ’1.5πœ‡πΌοŠ¦
  • E1.5πœ‡πΌοŠ¦

Evaluate ο…‡β‹…BId in terms of πœ‡οŠ¦ and 𝐼 for path 𝐷.

Q3:

A nonconducting hard rubber circular disk of radius 20.0 cm is painted with a uniform surface charge density 1.00 C/m2. It is rotated about its axis with angular speed 400 rad/s. find the magenetic field produced at a point on the axis a distance 2.00 cm from the center of the disk.

  • A4.20Γ—10 T
  • B3.96Γ—10 T
  • C4.44Γ—10 T
  • D3.82Γ—10 T
  • E2.04Γ—10 T

Q4:

The figure shows a cross section of a long hollow cylindrical conductor of inner radius π‘Ÿ=4.0cm and outer radius π‘Ÿ=8.0cm. A 150 A current distributed uniformly over the cross section flows into the page. Consider the permeability of the conductor to be 1.25Γ—10 H/m.

Calculate the magnetic field at π‘Ÿ=3.0cm.

Calculate the magnetic field at π‘Ÿ=6.0cm.

  • A3.8Γ—10 T
  • B3.1Γ—10 T
  • C2.08Γ—10οŠͺ T
  • D1.4Γ—10 T
  • E0.32Γ—10 T

Calculate the magnetic field at π‘Ÿ=10.0cm.

  • A5.0Γ—10οŠͺ T
  • B3Γ—10οŠͺ T
  • C9.6Γ—10οŠͺ T
  • D4.6Γ—10οŠͺ T
  • E7.8Γ—10οŠͺ T

Q5:

A superconducting wire of diameter 50.0 cm carries a current of 2,000 A. What is the magnetic field just outside the wire?

  • A4.92Γ—10οŠͺ T
  • B8.02Γ—10οŠͺ T
  • C9.02Γ—10οŠͺ T
  • D13.0Γ—10οŠͺ T
  • E98.6Γ—10οŠͺ T

Q6:

Use Ampere’s law to evaluate ο…‡β‹…Bld for the current configurations and paths shown in each of the following figures.

  • A1Γ—10 Tβ‹…m
  • B0.9Γ—10 Tβ‹…m
  • C1Γ—10 Tβ‹…m
  • D0.6Γ—10 Tβ‹…m
  • E5Γ—10 Tβ‹…m
  • A1Γ—10 Tβ‹…m
  • B0.5Γ—10 Tβ‹…m
  • C10Γ—10 Tβ‹…m
  • D5Γ—10 Tβ‹…m
  • E3Γ—10 Tβ‹…m
  • A0.1Γ—10 Tβ‹…m
  • B50Γ—10 Tβ‹…m
  • C0 Tβ‹…m
  • D0.4Γ—10 Tβ‹…m
  • E2Γ—10 Tβ‹…m
  • A0.7Γ—10 Tβ‹…m
  • B0 Tβ‹…m
  • C5Γ—10 Tβ‹…m
  • D0.5Γ—10 Tβ‹…m
  • E1Γ—10 Tβ‹…m
  • A0.9Γ—10 Tβ‹…m
  • B0.3Γ—10 Tβ‹…m
  • C0.1Γ—10 Tβ‹…m
  • D20Γ—10 Tβ‹…m
  • E9.0Γ—10 Tβ‹…m

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