4 1 The picture above shows a cross-section through three long straight parallel

Question

4 1 The picture above shows a cross-section through three long straight parallel wires, numbered 1, 2, and 3, which pass through different corners of a square. Remember that an X means the current is directed into the screen, and a dot (or circle) means the current is directed out of the screen. The fourth corner of the square is labeled with the number 4, but there is no wire there. The arrows on each wire show the net force being exerted on that wire by the other two wires. Note that that net force on wire 1 is at an angle of exactly 45 degrees to the horizontal, and the net force on wire 2 has no horizontal component.

Explanation / Answer

from the given problem

a. as the net force on the particel si along the arrow, and the current is into the page

hence from left hand rule

the magnetic eld is to the right at the location of the wire 2

b. i3 = 5.2 A

c. i1 = 2.6 A

now B2 = 10*10^-6 T i

B1 = 2ki1(cos(45)i - sin(45)j)/a*sqrt(2)

B3 = 2ki3/a j

10^10^-6 = 2k*i2/a

also, 2ki2/a = 2ki3/a

hence

i2 = i3 = 5.2 A

hence

a = 0.104 m

hence

B = B1 + B2 + B3 = 0.000005(i - j) + 10^-5 i + 0.00001 j

B = 15*10^(-6)i + 5*10^-6 j

|B| = 15.811*10^-6 T

d. magnetic field at the center of the loop = 2*k*sqrt(2)sqroot((i3 + i2)^2 + i1^2)/d

Bc = 29.15475 *10^-6 T

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