Biot-Savart's law of magnetic field electromagnetic fields

[Alhussein]

Biot-Savart's law of magnetic field " electromagnetic fields"

Homework Statement

A rectangular loop carrying 10 A of current is placed on z=0 plane as shown in figure . Evaluate H at a) (2,2,0)
b) (4,2,0)
c) (4,8,0)
d) (0,0,2)

Homework Equations

the used equation to answer the problem is
H= I/4∏ρ * (cosθ2-cosθ1) a∅
where ρ is the perpendicular distance between the line carrying current and the point which we need to evaluate H at
a∅=al X aρ
where aρ is a unit vector along the perpendicular line from the line current to the field point

The Attempt at a Solution

i already answered a,b,c and I'm sure about the answers
but the number d is kinda hard . i solved it with many ways but it seems that I'm misunderstanding something here so i hoped that some1 can help me and tell me
what's the ρ and aρ is this situation . i just need to know how to get ρ and aρ in the future so i hope whoever answers will concentrate on showing me how to get it . thanks for helping me

http://www.mediafire.com/?21cwcskwt3yect4

 

[SammyS]

Homework Statement

A rectangular loop carrying 10 A of current is placed on z=0 plane as shown in figure . Evaluate H at a) (2,2,0)
b) (4,2,0)
c) (4,8,0)
d) (0,0,2)

Homework Equations

the used equation to answer the problem is
H= I/4∏ρ * (cosθ2-cosθ1) a∅
where ρ is the perpendicular distance between the line carrying current and the point which we need to evaluate H at
a∅=al X aρ
where aρ is a unit vector along the perpendicular line from the line current to the field point

The Attempt at a Solution

i already answered a,b,c and I'm sure about the answers
but the number d is kinda hard . i solved it with many ways but it seems that I'm misunderstanding something here so i hoped that some1 can help me and tell me
what's the ρ and aρ is this situation . i just need to know how to get ρ and aρ in the future so i hope whoever answers will concentrate on showing me how to get it . thanks for helping me

http://www.mediafire.com/?21cwcskwt3yect4

Your image is NOT viewable. I don't see it !

 

[Alhussein]

Your image is NOT viewable. I don't see it !

sry here's the picture. it's kinda small idk why. anyway in words the current goes from origin to point (8,0) then from point (8,0) to (8,4) then from point (8,4) to (0,4) then it goes from point (0,4) back to origin

 

[cupid.callin]

Let the loop is ABCD
look at the above pic, By finding the angle of B and B_net, you can find net mag field

 

[asteriatic]

Biot-Savart's law of magnetic field states that a magnetic field is generated by a current-carrying wire and is proportional to the magnitude of the current, the length of the wire, and the sine of the angle between the wire and the point where the magnetic field is being measured. This law is fundamental in understanding the behavior of electromagnetic fields and is used in many applications in physics and engineering.

In this problem, we are asked to evaluate the magnetic field at four different points in space, given a rectangular loop carrying 10 A of current placed on the z=0 plane. To do this, we can use the equation provided, which is based on Biot-Savart's law.

For point (0,0,2), we need to determine the perpendicular distance between the line carrying current and the point. In this case, the perpendicular distance is simply the distance between the z=0 plane and the point, which is 2 units. This is our ρ value.

Next, we need to determine the unit vector aρ, which is a vector that points from the line carrying current to the field point and is perpendicular to both the line and the direction of current flow. In this case, since the line carrying current is on the z=0 plane, aρ will be in the z direction. Therefore, aρ = (0,0,1).

Plugging in these values into the equation provided, we get:

H = (10 A)/(4π * 2 units) * (cos90° - cos0°) * (0,0,1)

H = (10 A)/(8π) * (0 - 1) * (0,0,1)

H = (-5/4π) * (0,0,1)

H = (0,0,-5/4π)

Therefore, at point (0,0,2), the magnetic field is (0,0,-5/4π).