Question

A long wire carrying a 4.0 A current perpendicular to the xy-plane intersects the x-axis at x=−2.2cm. A second, parallel wire carrying a 2.8 A current intersects the x-axis at x=+2.2cm

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

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

Answer #1

**let**

**I1 = 4 A**

**I2 = 2.8 A**

**A) when the two currents are in the same direction, in
between the wires the magnetic field direction are opposite to each
other.**

**let at x cm from Origin Bnet = 0**

**B1 = B2**

**mue*I1/(2*pi*(2.2+x)) =
mue*I2/(2*pi*(2.2-x))**

**4/(2.2+x) = 2.8/(2.2 - x)**

**x = 0.39 cm**

**B) A) when the two currents are in the opposite
direction, in between the wires the magnetic field direction is in
the same direction.**

**so, the point where Bnet is zero will be beyond +2.2
cm**

**let at x cm from Origin Bnet = 0**

**B1 = B2**

**mue*I1/(2*pi*(2.2+x)) =
mue*I2/(2*pi*(x-2.2))**

**4/(2.2+x) = 2.8/(x-2.2)**

**x = 12.5 cm (on rounding 12 cm)**

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