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
  • B βˆ’ 1 . 3 πœ‡ 𝐼 
  • C 1 . 3 πœ‡ 𝐼 
  • D 3 πœ‡ 𝐼 
  • E 1 . 7 πœ‡ 𝐼 

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
  • B βˆ’ 5 πœ‡ 𝐼 
  • C 2 . 6 πœ‡ 𝐼 
  • D 3 . 5 πœ‡ 𝐼 
  • E 7 πœ‡ 𝐼 

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

  • A0
  • B βˆ’ πœ‡ 𝐼 
  • C βˆ’ 2 πœ‡ 𝐼 
  • D 2 πœ‡ 𝐼 
  • E πœ‡ 𝐼 

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.

  • A βˆ’ πœ‡ 𝐼 
  • B πœ‡ 𝐼 
  • C 1 . 5 πœ‡ 𝐼 
  • D βˆ’ 1 . 5 πœ‡ 𝐼 
  • 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.

  • A πœ‡ 𝐼 
  • B0
  • C βˆ’ πœ‡ 𝐼 
  • D βˆ’ 1 . 5 πœ‡ 𝐼 
  • E 1 . 5 πœ‡ 𝐼 

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.

  • A 4 . 2 0 Γ— 1 0   T
  • B 3 . 9 6 Γ— 1 0   T
  • C 4 . 4 4 Γ— 1 0   T
  • D 3 . 8 2 Γ— 1 0   T
  • E 2 . 0 4 Γ— 1 0   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.

  • A 3 . 8 Γ— 1 0   T
  • B 3 . 1 Γ— 1 0   T
  • C 2 . 0 8 Γ— 1 0  οŠͺ T
  • D 1 . 4 Γ— 1 0   T
  • E 0 . 3 2 Γ— 1 0   T

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

  • A 5 . 0 Γ— 1 0  οŠͺ T
  • B 3 Γ— 1 0  οŠͺ T
  • C 9 . 6 Γ— 1 0  οŠͺ T
  • D 4 . 6 Γ— 1 0  οŠͺ T
  • E 7 . 8 Γ— 1 0  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?

  • A 4 . 9 2 Γ— 1 0  οŠͺ T
  • B 8 . 0 2 Γ— 1 0  οŠͺ T
  • C 9 . 0 2 Γ— 1 0  οŠͺ T
  • D 1 3 . 0 Γ— 1 0  οŠͺ T
  • E 9 8 . 6 Γ— 1 0  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.

  • A 1 Γ— 1 0   Tβ‹…m
  • B 0 . 9 Γ— 1 0   Tβ‹…m
  • C 1 Γ— 1 0   Tβ‹…m
  • D 0 . 6 Γ— 1 0   Tβ‹…m
  • E 5 Γ— 1 0   Tβ‹…m
  • A 1 Γ— 1 0   Tβ‹…m
  • B 0 . 5 Γ— 1 0   Tβ‹…m
  • C 1 0 Γ— 1 0   Tβ‹…m
  • D 5 Γ— 1 0   Tβ‹…m
  • E 3 Γ— 1 0   Tβ‹…m
  • A 0 . 1 Γ— 1 0   Tβ‹…m
  • B 5 0 Γ— 1 0   Tβ‹…m
  • C0 Tβ‹…m
  • D 0 . 4 Γ— 1 0   Tβ‹…m
  • E 2 Γ— 1 0   Tβ‹…m
  • A 0 . 7 Γ— 1 0   Tβ‹…m
  • B0 Tβ‹…m
  • C 5 Γ— 1 0   Tβ‹…m
  • D 0 . 5 Γ— 1 0   Tβ‹…m
  • E 1 Γ— 1 0   Tβ‹…m
  • A 0 . 9 Γ— 1 0   Tβ‹…m
  • B 0 . 3 Γ— 1 0   Tβ‹…m
  • C 0 . 1 Γ— 1 0   Tβ‹…m
  • D 2 0 Γ— 1 0   Tβ‹…m
  • E 9 . 0 Γ— 1 0   Tβ‹…m

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