Problem 5: A circular arc of wire with radius R and extent from 01 to 02 carries a current I as shown in the diagram to the right. (You may assume that this arc of wire is part of a larger circuit that may be ignored for the purposes of this exercise.) You will calculate the magnetic field at the point P by evaluating a Biot-Savart integral of the form Ids x r 47 p2 R, Part (a) Enter an expression for the current element I ds. Expression : I ds = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), ɛo, µo, T, 01, 02, î, j, k, de, dr, I, p, R Part (b) With the origin of your coordinate system placed at the observation point P, enter an expression for the unit vector r. Expression : r = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), ɛo, µo, T, 01, 02, î, j, k, d0, dr, I, p, R Part (c) With the origin of your coordinate system placed at the observation point P, which integral provides a correct evaluation of the magnetic field at P? (Make no simplifications at this step.) MultipleChoice : IRde(- sin(@) i +cos (0) § ) × (- cos(0) i -sin(0) ĵ Ho 1) R I Rde(- sin(8) i +cos(0) } ) ×(- cos(0) i -sin(8) } ) R IRde (sin(8) i +cos(@) 3 ) ×(- cos(0) i -sin(0) j ) 4т B = S 2) 3) B = So R c2m IRde(- sin(0) i +cos(8) )x(- cos(0) i -sin(0) } ) R 4) В IRde (- sin(e) î +cos(0) 3 ) × (- cos(0) î – sin(e) 3 ) IRde(- sin(8) î +cos(0) ) x (- cos(0) i -sin(0) } 5) 4T Ho 6) B = 4т IRde(- sin(0) i +cos(0) )× (cos(0) i -sin(8) ĝ 7) Ho B = AT R IR10(- sin(0) i +cos(8) )x (cos(8) i +sin(8) 一与

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Can you please answer a,b & c?

Problem 5: A circular arc of wire with radius R and extent from 01 to 02 carries a
current I as shown in the diagram to the right. (You may assume that this arc of wire
is part of a larger circuit that may be ignored for the purposes of this exercise.) You
will calculate the magnetic field at the point P by evaluating a Biot-Savart integral of
the form
Idš x î
47
p2
R,
Part (a) Enter an expression for the current element I ds.
Expression :
Ids =
Select from the variables below to write your expression. Note that all variables may not be required.
cos(0), sin(0), ɛo, µo, T, 01, 02, î, ĵ, k, d0, dr, I, p, R
Part (b) With the origin of your coordinate system placed at the observation point P, enter an expression for the unit
vector r.
Expression :
r =
Select from the variables below to write your expression. Note that all variables may not be required.
cos(0), sin(0), ɛo, µo, T, 01, 02, î, j, k, d0, dr, I, p, R
Part (c) With the origin of your coordinate system placed at the observation point P, which integral provides a correct
evaluation of the magnetic field at P? (Make no simplifications at this step.)
MultipleChoice :
IRde(- sin(0) i +cos(0) j ) × (- cos(0) i -sin(8) ĵ
Ho
1)
R
IRde(- sin(8) î +cos(8) § ) × (- cos(8) i -sin(8) })
R
IRde (sin(@) i +cos(@) § ) × (- cos(0) î -sin(0) j )
4т
B = S
Ho
2)
3) B = So
R?
c2m IRde(- sin(0) i +cos(8) )x(- cos(0) i -sin(8) } )
R
4)
В
Ho
IRde (- sin(e) î +cos(8) 3 ) × (- cos(0) î – sin(e) § )
Ho
5)
4T
IRde(- sin(0) i +cos(0) ) x(- cos(8) i -sin(0)
Ho
6)
B =
4т
IRde(- sin(0) i +cos(0) )× (cos(0) i -sin(8) ĝ
7)
B =
R2
IRde(- sin(@) î +cos(0) § ) × (cos(0) i +sin(8) })
8)
R2
Part (d) With the origin of your coordinate system placed at the observation point P, which partially simplified integral
provides a correct evaluation of the magnetic field at P?
MultipleChoice :
-Sa cos²(8)de k
S do k
1)
B =
2)
B =
4nR
g So, (sin (0) – cos² (0)) do :
-S sin? (0)de k
3) В
B =
4R
HoI
B =
ER Je, 2 sin(0) cos(0)de
4)
5)
6)
Sr de k
4TR Je,
So cos?(0)do k
B =
4TR
B
7)
8)
4R Jo, sin? (0)de î:
Part (e) Evaluate the integral and enter a simplified expression for the magnitude of the magnetic field, B, evaluated at P.
Expression :
B =
Select from the variables below to write your expression. Note that all variables may not be required.
cos (θ), sin (θ), ερ, μ0, π, θ1, θ2 , 1j, k de, dr, L p, R
Part (f) Enter an expression for the direction of the magnetic field, B/B, evaluated at P.
Expression :
B/B =
Select from the variables below to write your expression. Note that all variables may not be required.
cos(0), sin(0), ɛo, µo, T, 0, 01, 02, î, ĵ, k, d0, dr, I, R
|| || || || || || |||
Transcribed Image Text:Problem 5: A circular arc of wire with radius R and extent from 01 to 02 carries a current I as shown in the diagram to the right. (You may assume that this arc of wire is part of a larger circuit that may be ignored for the purposes of this exercise.) You will calculate the magnetic field at the point P by evaluating a Biot-Savart integral of the form Idš x î 47 p2 R, Part (a) Enter an expression for the current element I ds. Expression : Ids = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), ɛo, µo, T, 01, 02, î, ĵ, k, d0, dr, I, p, R Part (b) With the origin of your coordinate system placed at the observation point P, enter an expression for the unit vector r. Expression : r = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), ɛo, µo, T, 01, 02, î, j, k, d0, dr, I, p, R Part (c) With the origin of your coordinate system placed at the observation point P, which integral provides a correct evaluation of the magnetic field at P? (Make no simplifications at this step.) MultipleChoice : IRde(- sin(0) i +cos(0) j ) × (- cos(0) i -sin(8) ĵ Ho 1) R IRde(- sin(8) î +cos(8) § ) × (- cos(8) i -sin(8) }) R IRde (sin(@) i +cos(@) § ) × (- cos(0) î -sin(0) j ) 4т B = S Ho 2) 3) B = So R? c2m IRde(- sin(0) i +cos(8) )x(- cos(0) i -sin(8) } ) R 4) В Ho IRde (- sin(e) î +cos(8) 3 ) × (- cos(0) î – sin(e) § ) Ho 5) 4T IRde(- sin(0) i +cos(0) ) x(- cos(8) i -sin(0) Ho 6) B = 4т IRde(- sin(0) i +cos(0) )× (cos(0) i -sin(8) ĝ 7) B = R2 IRde(- sin(@) î +cos(0) § ) × (cos(0) i +sin(8) }) 8) R2 Part (d) With the origin of your coordinate system placed at the observation point P, which partially simplified integral provides a correct evaluation of the magnetic field at P? MultipleChoice : -Sa cos²(8)de k S do k 1) B = 2) B = 4nR g So, (sin (0) – cos² (0)) do : -S sin? (0)de k 3) В B = 4R HoI B = ER Je, 2 sin(0) cos(0)de 4) 5) 6) Sr de k 4TR Je, So cos?(0)do k B = 4TR B 7) 8) 4R Jo, sin? (0)de î: Part (e) Evaluate the integral and enter a simplified expression for the magnitude of the magnetic field, B, evaluated at P. Expression : B = Select from the variables below to write your expression. Note that all variables may not be required. cos (θ), sin (θ), ερ, μ0, π, θ1, θ2 , 1j, k de, dr, L p, R Part (f) Enter an expression for the direction of the magnetic field, B/B, evaluated at P. Expression : B/B = Select from the variables below to write your expression. Note that all variables may not be required. cos(0), sin(0), ɛo, µo, T, 0, 01, 02, î, ĵ, k, d0, dr, I, R || || || || || || |||
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