why J=dI/da and the biot savart expression is an integral over the volume? If I manipulate the B=mu_0/(4pir^2) * i to dB=mu_0/(4pir^2) * dI= mu_0/(4pir^2) * J*da and integrate it gives a integral over the area not the volume.
This is a great question. I struggled with the concept of currents in multiple dimensions as well. In electronic circuits, it's simply a number, not a vector. The Biot-Savart Law takes into account ALL currents, flowing everywhere in space, in any direction, in any magnitude. You must integrate across all of space, measuring what the current is at each point in space. When you use other types of current you are excluding dimensions that are not relevant because they do not have current, or rather, skipping all the points in space that have zero current.
why is I written as a vector . Shouldnt current be a scalar quantity. I refered to the book but it says" but when it comes to surface and volume currents we cant be casual" ?
Idk if you need to know as it's been 3 years. Still here is my understanding. Current is a vector quantity, as these are charges in motion. It is more appropriate to talk about i•dl(dl is vector and i is scalar OR i is a vector and dl is scalar). When dealing with currents in wires, we can treat them as scalars, like how we say "speed" of a train even though it is the velocity, because the "direction of the speed" is the same as the direction of the track. So we can talk about the vector train•track (train is scalar, track is vector or the other way around). But if there is no wire and the train is sliding on a surface or floating in a volume we can't be casual and say "the speed of the train on the surface...". This time we must talk about its velocity that we just ignored in the case of motion along the track.
why is dl perpendicular to the flow? because in Griffith, the diagram shows dl parallel to flow and its written dl(perpndicular) for the formula of K! what's going on there?
Hi John. In the same section Griffth has treated electric current as a vector quantity. I=lamda* velocity. As current does not obey vector laws. How on earth Griffth has taken current as vector quantity. Can you help here.
@@sofiashaqhussain9919 How does it not follow vector addition? Two particles of the same velocity have a current twice the magnitude. Two particles crossing paths also form a current that is the vector sum of the motion. Find where it doesn't fit and let's pull it apart.
why J=dI/da and the biot savart expression is an integral over the volume? If I manipulate the B=mu_0/(4pir^2) * i to dB=mu_0/(4pir^2) * dI= mu_0/(4pir^2) * J*da and integrate it gives a integral over the area not the volume.
This is a great question. I struggled with the concept of currents in multiple dimensions as well. In electronic circuits, it's simply a number, not a vector. The Biot-Savart Law takes into account ALL currents, flowing everywhere in space, in any direction, in any magnitude. You must integrate across all of space, measuring what the current is at each point in space. When you use other types of current you are excluding dimensions that are not relevant because they do not have current, or rather, skipping all the points in space that have zero current.
Is the magnetic force is due to surface current or is the magnetic force on the surface current? Magnetic force due to what? Magnetic force on what?
why is I written as a vector . Shouldnt current be a scalar quantity. I refered to the book but it says" but when it comes to surface and volume currents we cant be casual"
?
Idk if you need to know as it's been 3 years. Still here is my understanding.
Current is a vector quantity, as these are charges in motion. It is more appropriate to talk about i•dl(dl is vector and i is scalar OR i is a vector and dl is scalar).
When dealing with currents in wires, we can treat them as scalars, like how we say "speed" of a train even though it is the velocity, because the "direction of the speed" is the same as the direction of the track. So we can talk about the vector train•track (train is scalar, track is vector or the other way around). But if there is no wire and the train is sliding on a surface or floating in a volume we can't be casual and say "the speed of the train on the surface...". This time we must talk about its velocity that we just ignored in the case of motion along the track.
@@dattatreyadas Damn I still cant believe I was reading this haha
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In surface current density why we divide it with perpendicular length??
Same in volume current density why we divide it with perpendicular area?
How dl is perpendicular to the flow?
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why is dl perpendicular to the flow? because in Griffith, the diagram shows dl parallel to flow and its written dl(perpndicular) for the formula of K! what's going on there?
I think its because the magnetic field always works with the cross product?
Hi John. In the same section Griffth has treated electric current as a vector quantity. I=lamda* velocity. As current does not obey vector laws. How on earth Griffth has taken current as vector quantity. Can you help here.
Moving charge is a current. Movement is a vector.
@@jg394 but John current does not obey laws of vector addition. These obey ordinary algebric laws. How about that?
@@sofiashaqhussain9919 How does it not follow vector addition? Two particles of the same velocity have a current twice the magnitude. Two particles crossing paths also form a current that is the vector sum of the motion. Find where it doesn't fit and let's pull it apart.
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@@jg394
The movement you refer in the first reply refers to velocity and that is obviously a vector.