Question

5.Two straight conductors are separated by a distance of 0.75 cm. If the first wire carries a current of 6.5 A towards the page, and the magnetic field of the two currents at a point P at 1.5 cm is zero, what current and direction must the second lead wire have for this to occur. Clarification (apart from the magnitude and the unit should say the direction of the current)

Answer 1

(Here the position of wires and point P is not specified. So i have assumed the the wire 1 is on the left, wire 2 on right and point p on right to both of them)

Suppose the current in second wire is I2. Distance from the second wire is, d2 = 1.5-0.75=0.75cm = 0.0075m

d1 = 1.5cm =0.015m

So Magnetic field at P is
B =μ0I1/2πd1 + μ0I2/2μd2
=(μ0/2π)(I1/d1 + I2/d2)

Given, B = 0
=> I1/d1 + I2/d2 = 0
=> I2 = - I1×d2/d1 = -6.5×0.0075/0.015
=-3.25A

Therefore the current in second wire is 3.25A coming out of the page.