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Question

http://t2.gstatic.com/images?q=tbn:ANd9GcRCal68MxcApCgBHoRLjzR1xW0XU7Na6EQ5i8zMEA-81t-C8l06R35Dbks08g

Two long horizontal straight parallel wires are 11.7 cm apart and each carries a current of 7.25 A in the directions shown in the above image.

a) What is the magnitude of the B-field at point P, which is at a perpendicular distance of 8.25 cm from both wires?

b) What is the direction of the B-field at point P?
Give the angle between the x-axis and the B-field in degrees with correct sig fig.
Thanks a lot!

Explanation / Answer

Magnetic Field by I1:

B1=oI1/2r

o=4*10^-7

B1=1.7576*10^-5 T (Perpendicular to line connecting I1and P)

Magnetic Field by I2:

B2=oI2/2r

o=4*10^-7

B2=1.7576*10^-5 T   (Perpendicular to line connecting I2and P)

(a)

Let mid-point of line I1 and I2 is M

I1M=I2M=11.7/2= 5.85 cm

angle(I1PM)=angle(I2PM) =arcsin(5.85/8.25) = 45.161 degree

Their X-component will cancel out each other.

We have only Y-component.

B(y-net)=B1 cos(45.161)+B2 cos(45.161)

=2.47863*10^-5 T or 2.48*10^-5 T

(B)

Direction =90 degree with x-axis Or 270 degree clockwise

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