Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

Show that the magnitude of magnetic induction at a point on the axis of a short bar magnet is twice the magnitude of magnetic induction at a point on the equator at the same distance.
Asked by kpbhake | 02 Mar, 2018, 09:49: AM
answered-by-expert Expert Answer
Let the length of barmagnet be 2l as shown in figure.  Let P be a point on the axis line at a distance d.
Magnetic induction at point P due to the poles of given barmagnet is given by

begin mathsize 12px style B subscript P space equals space fraction numerator mu subscript 0 over denominator 4 pi end fraction open parentheses m over open parentheses d minus l close parentheses squared space minus m over open parentheses d plus l close parentheses squared space close parentheses space equals fraction numerator mu subscript 0 over denominator 4 pi end fraction fraction numerator 4 l d space cross times m over denominator open parentheses d squared minus l squared close parentheses squared end fraction end style
where m is the pole strength of the given bar magnet. Let us assume d >> l and consider the magnetic moment = m×2l = M, then we can write the above relation as
begin mathsize 12px style B subscript P space equals space fraction numerator mu subscript 0 over denominator 4 pi end fraction fraction numerator 2 M over denominator d cubed end fraction end style.........................................(1)
Let Q be a point on the equatorial line at a distance d from bar-magnet as shown in figure. Magnetic induction at a point Q is given by
 
begin mathsize 12px style B subscript Q equals space 2 fraction numerator mu subscript 0 over denominator 4 pi end fraction fraction numerator m over denominator d squared plus l squared end fraction sin space theta space equals 2 fraction numerator mu subscript 0 over denominator 4 pi end fraction fraction numerator m over denominator d squared plus l squared end fraction fraction numerator l over denominator square root of d squared plus l squared end root end fraction space equals 2 fraction numerator mu subscript 0 over denominator 4 pi end fraction fraction numerator l space cross times m over denominator open parentheses d squared plus l squared close parentheses to the power of begin display style bevelled 3 over 2 end style end exponent end fraction end style
Refer the diagram for the desciption of the induction vectors due to the poles and how the reultant vector is worked out.

Again by considering magnetic moment M = m×2l and d >> l, we can wite the above expression as

begin mathsize 12px style B subscript Q equals space fraction numerator mu subscript 0 over denominator 4 pi end fraction M over d cubed end style..........................................(2)
from (1) and (2), we can write BP = 2×BQ
 
Answered by Thiyagarajan K | 02 Mar, 2018, 01:16: PM

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 12-science - Physics
a car battery of 12V as a current 7.5 a when 1.2 oh m load is applied find the internal resistance of the battery
Asked by heymindurownbusiness | 04 May, 2024, 11:15: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
superposition principle
Asked by talulu | 01 May, 2024, 05:14: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
question no. 7
question image
Asked by kanishkg511 | 30 Apr, 2024, 07:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
pls someone solve this
question image
Asked by sahoobanita89 | 30 Apr, 2024, 05:10: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
Electric sheilding 
Asked by divakar.9124 | 27 Apr, 2024, 10:42: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
explain this concept
question image
Asked by panneer1766 | 24 Apr, 2024, 01:52: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
A dumbbell consists of two masses A and B each of mass m joined by a light rod of length l with mass B attached to a suspension point O by a light rod of length l as shown in figure. Find the minimum required speed with which mass A to be projected horizontally so that the system completes the vertical circular motion.
question image
Asked by artabandhusahu85 | 24 Apr, 2024, 12:07: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
What is charge?
Asked by niharvijayvargiya5 | 23 Apr, 2024, 06:40: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
please resolve with good explanation
question image
Asked by kulhariabhijeet | 21 Apr, 2024, 02:39: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Physics
what are ghost particles please answer how is that not able to interact with other subatomic particles ..?is that faster than photons?
Asked by mohapatraswetalina88 | 21 Apr, 2024, 12:18: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×