Question

In the figure, two long straight wires at separation d = 7.12 cm carry currents of i1 = 5.51 mA and i2 = 7.00i1 out of the page. (a) At what coordinate on the x axis in centimeters is the net magnetic field due to the currents equal to zero? (b) If the two currents are doubled, is the zero-field point shifted toward wire 1, shifted toward wire 2, or unchanged?

Answer 1

(a)

as current from both wires is out of the page, net magnetic field can be zero only between the wires

let the distance be x from wire carrying current i2 then distance from wire carrying i2 becomes d - x.

so,

B1 = B2

u_o i1 / 2x = u_o * 7 * i1 / 2 ( d - x)

cancel all the like terms, we have

1/x = 7 / d-x

d-x = 7x

d = 8x

x = d / 8

x = 7.12 / 8

x = 0.89 cm

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(b)

Here, both currents are being doubled so,

zero field point remains UNCHANGED