PART A: In the figure(Figure 1) , find the magnitude of the magnetic field at po

Question

PART A: In the figure(Figure 1) , find the magnitude of the magnetic field at point A, which is located 9.0 cm away from wire 2 on a line perpendicular to the line joining the wires. Express your answer using two significant figures.

ANS is B = 1.4×10?5 T

Part B: Find the direction of the magnetic field at point A. Express your answer using two significant figures.

ANS is ? = 38 degrees below a horizontal line to the left

I have looked at other chegg post on this question but i dont understand. The following is the solution.

I get that the perm. of free space is in both B1 and B2 so it can be put out side the ( ). I get that the (2/9E-2) is the (I/r), ect. but why is B1's (I/R) included in the same ( ) as B2's? AND where does cos(45) and sin (45) come into play? WHy did this person use 9/5 as B1's ratio, shouldnt it be 9/12?

Explanation / Answer

field by wire 2 only in horizontal

B = uo*I2/2pir2

r2 = 9 m

now on point A by wire 1

there is 2 component of force and they are in horizontal and vertical

x componet is = uo*I1*costheta/2pir1

y componet is = uo*I1*I2*sintheta/2pir1

r1 = distance which is making right angle

r1 = sqrt(x^2+y^2)

x = 12 , y = 9

now add them because thet are in same direction

B = Bi + Bj

so magnitude of B = sqrt(Bi^2+Bj^2)

theta = tan^-1(Bj/Bi)

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