x = + 2.0 c m Part A At what point on the x -axis is the magnetic field zero if

Question

x=+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.

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

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

Explanation / Answer

let I1 = 5.5 A, I2 = 3.5 A

here I1 > I2.

so the point where the Bnet = 0 is close to second wire

distance between two wire, d = 2+2 = 4 cm

let at a distance r from second wire, B1 = B2

B1 = B2

mue*I1/(2*pi*(d+r) = mue*I2/(2*pi*r)

I1/(d+r) = I2/r

5.5/(4+r) = 3.5/r

5.5*r = 3.5*5.5 + 3.5 r

==> r = 19.25/2 = 9.625 cm

so, at x = 2 + 9.625 = 11.625 cm, Bnet = 0

case 2)

B1 = B2

mue*I1/(2*pi*(d-r) = mue*I2/(2*pi*r)

I1/(d-r) = I2/r

5.5/(4-r) = 3.5/r

5.5*r = 3.5*5.5 - 3.5 r

==> r = 19.25/9 = 2.138 cm

so, at x = 2 - 2.139 = -0.139 m Bnet = 0

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