A long wire carrying a 6.0 A current perpendicular to the xy -plane intersects t

Question

A long wire carrying a 6.0 A current perpendicular to the xy-plane intersects the x-axis atx=2.0cm. A second, parallel wire carrying a 3.5 A current intersects the x-axis atx=+2.0cm.

Part A

At what point on the x-axis is the magnetic field zero if the two currents are in the same direction?

Express your answer using two significant figures.

Part B

At what point on the x-axis is the magnetic field zero if the two currents are in opposite directions?

Express your answer using two significant figures.

Explanation / Answer

here I1 = 6 A r1 = - 2 cm = - 0.02 m

I2 = 3.5A r2 = 2 cm = 0.02 m

so the two wire are placed at distance r = 0.04 m

(A) if the two current are same direction

let at point m magnatic field is zero

so during first wire   

B1 = uo I1 / 2 x pi x m

= 4 x 3.14 x 10-7 x 6 / 2 x 3.14 x m inside the plane

= 12 x 10-7 / m (inside the plane)

during to second wire

B2 = uo I2 / 2 x pi x (0.04 - m )

= 4 x 3.14 x 10-7 x 3.5 / 2 x 3.14 x (0.04 - m)

= 7 x 10-7 / (0.04 - m)  (outside the plane)

so according to question

B = 0

here both B are in opposite direction

B1 = B2

12 x 10-7 / m = 7 x 10-7 / (0.04 - m)

0.48 - 12m = 7m

m = 0.02526 meter Ans

(B) if the two current are in opposite direction

B1 = 12 x 10-7 / m (inside the plane)

B2 = 7 x 10-7 / (0.04 - m) (inside the plane)

so B = 0

here both B are in same direction

B1 = - B2

12 / m = - 7 / (0.04 - m)

0.48 - 12m = -7m

m = 0.096 meter Ans

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