Biot Savart law (vector form) | Moving charges & magnetism | Khan Academy
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- Опубліковано 18 бер 2021
- Biot Savart law states that the magnetic field due to a tiny current element at any point is proportional to the length of the current element, the current, the sine of the angle between the current direction and the line joining the current element and the point, and inversely proportional to the square of the distance of that point.
The direction of the magnetic field is in the direction of dl cross r. You can also use the right hand clasp rule to figure out the direction.
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Created by Mahesh Shenoy
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For each tiny segment, do we have to do a vector sum?
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Isn’t this finding just the magnetic field as it is affected by the length of dl? So to find the total force applied on a single point you would need to do multiple equations? Or should you just use the perpendicular measurement (since it is where force is strongest) for an estimate?
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Sir one doubt, in the textbook and other sources the vector form of Biot-Savart law has r^(3) but yours is r^(2)... Can you please clear my doubt??
You have to use r^3 if you dont use the unit vector. the guy used unit vectors which is why he uses r^2. for more info you can look at the english wikipedia article about biot-savart
@@felixwegmuller351 Thank you ☺️
@@user-cc7ks7re3w the other explained it pretty well, you can either use unit vector in the direction of radius to denote the vector for radius, or just simplify the unit vector which turns out to be
*r* /r , plug this value instead of unit vector and you'll get the textbook equation
Watching this before 6 hours before exam (time:-1:54AM) 😀
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0:01
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Sir in NCERT it is given that in vector form the distance is r^3 but you mentioned it as r^2...please clarify it
We know r is a unit vector
So, r^ = r(vector)/ |r|
Or, r^ = r(vector)/r
Since, |r| = r
So, put the value of r^ then you get r³
Why is it r^3 in my textbook not r^2..
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Hey here's a doubt, our NCERT books say idl*r^
^3 but u hv written r^2 instead of r^3 so which one's right?
hello kaushik rcap can also be said as r vector . r = so it becomes rvector / r^3
Did you mean by substituting r cap=(r vector/magnitude of r vector)?
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I appreciate your efforts.
But you lacked in explaining why magnetic field changes when we change angle. You just explained the effect but skipped the cause...!
Watch previous videos.
In India we pronounced as it is given in book like biot savart law 😅😅
why only dl vector cross r vector why not r vector cross dl vector. Could anyone explain or which one of your videos explain this?
Concept: Vectors - Cross Product
Suppose we have two vectors,
A=2i+3j and B=4i−j where i and j are unit vectors along the x and y axes, respectively.
The cross product
A×B is given by:
A×B= ∣ i j k ∣
2 3 0
4 -1 0
Now, calculating the cross product;
A×B=(3×0−(−1)×0)i−(2×0−4×0)j+(2×(−1)−3×4)k
we get:
AxB =0i-0j-12k
A×B= −12k. [It is in the negative z- axis]
But in this case if we do B x A:
By doing the same method again as shown above but putting values accordingly.
Mathematically the relationship is expressed as:
B x A = - ( A x B )
A x B= -12 (as calculated)
B X A = - (-12k)
= +12k [it is in Positive Z axis]
Difference in the direction!! Similarly, we cannot write r x dl.
Why you take DL as a vector??? (Length is scalar) 😅
Extraclear, extraexplained extrasimple
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the real problem is he drew the direction of the current in a wrong direction.
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Why (dl × r ).not (r × dl)
Sorry, i do not know in detail 😅 . What i know is, in cross product, the order matters. The direction of the magnetic field will change if u take (r x dl) instead of (dl x r). The direction will be in accordance with the "right hand rule". if u take (r x dl), your magnitude will be the same, but your direction will be opposite to that of the right hand rule. Thats what i know😅.
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I give up already...maybe cause I've got no idea about vectors and I'm supposed to be doing this chapter as I'm in class 10...but I have to do all these complex things because they are important for competitive exams...why do they do this to us...😭😭
Electromagnetics is hard bro, just keep pushing and grinding through. You got this