General Physics 2 Activity Sheet
Quarter 4 – MELC 4
Week 1
Magnetic Field Vector at Any Point
Along the Axis of Circular Current
Loop
REGION VI – WESTERN VISAYAS
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General Physics 2
Activity Sheet No.4 : Magnetic Field Vector at Any Point Along the Axis of
Circular Current Loop
First Edition, 2021
Published in the Philippines
By the Department of Education
Region 6 – Western Visayas
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This Learning Activity Sheet is developed by DepEd Region 6 – Western
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or transmitted in any form or by any means electronic or mechanical without written
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Development Team of General Physics 2 Activity Sheet
Writer: Joemarie S. Selibio
Editors: Jave N. Salinas
Glenn Mark D. Fallera
Schools Division Quality Assurance Team:
Mary Regina N. Alkonga
Noemi A. Salvador
Stella J. Tacuyan
Division of Iloilo City Management Team:
Ma. Luz M. De Los Reyes
Ernesto F. Servillon Jr.
Arlo L. Villalva
Leila G. Valencia
Regional Management Team:
Ramir B. Uytico
Pedro T. Escobarte, Jr.
Elena P. Gonzaga
Donald T. Genine
Rovel R. Salcedo
Moonyeen C. Rivera
Anita S. Gubalane
Minda L. Soldevilla
Daisy L. Lopez
Joseph M. Pagalaran
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Introductory Message
Welcome to General Physics 2 for Grade 12!
The Learning Activity Sheet is a product of the collaborative efforts of the
Schools Division of Iloilo City and DepEd Regional Office VI - Western Visayas through
the Curriculum and Learning Management Division (CLMD). This is developed to guide
the learning facilitators (teachers, parents and responsible adults) in helping the
learners meet the standards set by the K to 12 Basic Education Curriculum.
The Learning Activity Sheet is self-directed instructional materials aimed to
guide the learners in accomplishing activities at their own pace and time using the
contextualized resources in the community. This will also assist the learners in
acquiring the lifelong learning skills, knowledge and attitudes for productivity and
employment.
For learning facilitator:
The General Physics 2 Activity Sheet will help you facilitate the teachinglearning activities specified in each Most Essential Learning Competency (MELC) with
minimal or no face-to-face encounter between you and learner. This will be made
available to the learners with the references/links to ease the independent learning.
For the learner:
The General Physics 2 Activity Sheet is developed to help you continue
learning even if you are not in school. This learning material provides you with
meaningful and engaging activities for independent learning. Being an active learner,
carefully read and understand the instructions then perform the activities and answer
the assessments. This will be returned to your facilitator on the agreed schedule.
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Name of Learner:
___________________________________________________
Grade and Section:_______________________________Date: ________________
GENERAL PHYSICS 2 ACTIVITY SHEET No. 4
Magnetic Field Vector at Any Point Along the Axis of
Circular Current Loop
I.
Learning Competency with Code
Evaluate the magnetic field vector at any point along the axis of a circular current
loop. STEM_GP12EMIIIi-64
II. Background Information for Learners
Considering that a magnetic field is produced by introducing current on a
circular loop, the Biot-Savart law is considered once again. At any particular point
in a circular loop, it is possible for you to determine the magnitude of magnetic
field produced by taking into consideration the angles and the use of some
trigonometric functions. Your investigation could also take into consideration the
3 -dimensional axis as well as the use of the right-hand rule in determining the
direction of the produced magnetic field.
III.
Activity Proper
Activity 1
Directions:
• Consider the important ideas and sample problems presented
• Perform the task required.
• Analyze and answer the guide questions.
Magnetic Field Produced by a Current on Circular Loop
If a current-carrying wire were formed into a circular loop, how would
this change the direction of the magnetic field? Consider Figure 1 below, where
a circular loop is acted upon by a current I. You could evaluate a portion of
magnetic field P considering a 3-dimensional axis x, y, and z which are
perpendicular to one another Using Biot-Savart Law.
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Figure 1. A current carrying loop with a magnetic field evaluated at point P along the
z-axis.
You can take a small portion of a circular loop t ⃗⃗⃗
𝑑𝑙 and evaluate its part in
⃗⃗⃗⃗⃗
producing a portion of magnetic field 𝑑𝐵 at point P along the z-axis. From the center
C the magnetic field to be evaluated is at point P which is at a distance z along the z
⃗ . The portion of the magnetic
axis. It should be noted also that ⃗⃗⃗
𝑑𝑙 is perpendicular to ℎ
field ⃗⃗⃗⃗⃗
𝑑𝐵 at point P on the other hand, is the result of the superposition of two magnetic
fields which are along y and along z.
Biot-Savart Law provides a formula in determining the magnitude of magnetic
field at point P which is
𝜇𝑜 𝐼 𝑑𝑙
𝑑𝐵 = ( )( 2 )
4𝜋 ℎ
Considering the Pythagorean Theorem 𝑐 2 = 𝑎2 + 𝑏2 , you can derive the
equation of ℎ = 2√𝑧 2 + 𝑦 2. Using this in the equation results to
𝑑𝐵 = (
𝜇𝑜 𝐼
𝑑𝑙
)( 2
)
4𝜋 𝑧 + 𝑦 2
You can determine the components of the vector ⃗⃗⃗⃗⃗
𝑑𝐵 using your
knowledge on trigonometric functions and obtain
𝜇 𝐼
𝑑𝑙
𝑦
𝑜
𝑑𝐵𝑧 = 𝑑𝐵 𝑐𝑜𝑠𝜃 = ( 4𝜋
) (𝑧 2 +𝑦2 ) ( 2
√𝑧 2 +𝑦 2
𝑑𝐵𝑦 = 𝑑𝐵 𝑐𝑜𝑠𝜃 = (
𝜇𝑜 𝐼
4𝜋
)(
𝑑𝑙
𝑧 2 +𝑦 2
)( 2
𝑧
√𝑧 2 +𝑦2
) and
)
⃗⃗⃗ , say on the opposite
If you however consider the contribution of other elements 𝑑𝑙
side of the circular loop, it will produce a value that will cancel the effect of the other
component of magnetic field.
To obtain the value of magnetic field along z, you can consider all the element
⃗⃗⃗
𝑑𝑙 ′𝑠 around a circular loop and using an integration process. In which the ∫ 𝑑𝑙 = 2𝜋𝑦
where y is the radius of the circular loop. Thus, you obtain,
2
𝐵𝑧 = (
𝜇𝑜 𝐼𝑦 2
3)
(𝑜𝑛 𝑡ℎ𝑒 𝑎𝑥𝑖𝑠 𝑜𝑓 𝑎 𝑐𝑖𝑟𝑐𝑢𝑙𝑎𝑟 𝑙𝑜𝑜𝑝)
2(𝑧 2 + 𝑦 2 )2
On this case, it is important to note that the right-hand rule is still applied to
determine the direction of magnetic field around a circular loop.
Sample Problem
Using the formula 𝐵𝑧 = (
𝜇𝑜 𝐼𝑦2
3
) determine what will happen to the value of Bz if the
2(𝑧2 +𝑦2 )2
magnitude of current I is reduced to half of its original value while keeping other
variables constant.
Solution
𝜇𝑜 𝐼𝑦2
With a formula 𝐵𝑧 = (
3
) you could infer by keeping all other
2(𝑧2 +𝑦2 )2
variables constant that
𝐵𝑧 𝛼 𝐼 . Therefore, if you reduce the value of current (I) to half of its original
value the z-component of Magnetic field will also be reduced by half of its
original value.
1
2
1
𝐼 𝑤𝑖𝑙𝑙 𝑟𝑒𝑠𝑢𝑙𝑡 𝑡𝑜 2 𝐵𝑧
Task 1: Evaluating the Relationship of Bz and the Current (I)
A. Using the formula 𝐵𝑧 = (
𝜇𝑜 𝐼𝑦2
3
) complete the table below by predicting
2(𝑧2 +𝑦2 )2
the effect of one variable to another variable while keeping other variables
constant.
µ𝒐
I
Ampere
z
(meter)
y
(meter)
µ𝒐
2I
Z
y
Bz
(Tesla)
1.________
µ𝒐
Z
y
3Bz
3.________
2._______
µ𝒐
½I
Z
y
µ𝒐
4._______
Z
y
3
¼ Bz
Guide Questions
1. What will happen to the value of Bz if current (I) is increased?
______________________________________________________________
______________________________________________________________
2. How will you describe the relationship that exist between the Magnitude of B z
and the amount of Current?
______________________________________________________________
______________________________________________________________
IV.
Reflection
I understand
___________________________________________________________
___________________________________________________________
I don’t understand
___________________________________________________________
___________________________________________________________
I need more information about
___________________________________________________________
___________________________________________________________
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Answer Key
4. ¼ I
µ𝒐
½I
µ𝒐
2. 3I
µ𝒐
y
z
y
z
y
z
V.
¼ Bz
3. ½ Bz
3Bz
1. 2 Bz
µ𝒐
µ𝒐
2I
z
I
Ampere
z
(meter)
y
y
(meter)
Bz
(Tesla)
2. How will you describe the relationship that exist between the Magnitude of Bz and
the amount of Current?
Ans. They are Directly Proportional
__________________________________________________________________________
__________________________________________________________________
1. What will happen to the value of Bz if current (I) is increased?
Ans. It will also increase
2. Guide Questions
VI. Links and Other References
“Resnick, Halliday, Krane: Physics, Volume 1, 5th Edition - Student Companion
Site.”
Wiley.com,2021.http://bcs.wiley.com/hebcs/Books?action=index&itemId=04713
20579&itemTypeId=BKS&bcsId=1458.
book-info.com – Sascha Hendel. “3,000 Solved Problems in Physics –
Schaum’s Solved Problems Series [McGraw-Hill: First Edition].” book-info.com,
2011. https://www.book-info.com/isbn/0-07-025734-5.htm.
“University Physics with Modern Physics | Hugh D. Young, Roger A. Freedman
| Download.” 1lib.ph. Z-Library, 2015.
https://1lib.ph/book/604468/daf477?regionChanged=&redirect=182684539.
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“Physics for Scientists & Engineers : Serway, Raymond a : Free Download,
Borrow, and Streaming : Internet Archive.” Internet Archive, 2014.
https://archive.org/details/physicsforscient00serw.
Janzen, Daryl. “9.4 Magnetic Field of a Current Loop.” Usask.ca. University
of Saskatchewan, Distance Education Unit, November 28, 2018.
https://openpress.usask.ca/physics155/chapter/9-4-magnetic-field-of-acurrent-loop/.
teachoo. “Magnetic Field due to a Current through a Circular Loop - Class
10.” teachoo, August 2019. https://www.teachoo.com/10698/3113/Magneticfield-due-to-a-Current-through-a-Circular-Loop/category/Concepts/.
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