Question

Two parallel wires P and Q placed at a separation $d=6m$ carry electric currents $i_1=5A$ and $i_2=2A$ in opposite direction as shown in figure. Find the point on the line PQ where the resultant magnetic field is zero

• A. 2 cm from Q
• B. 4 cm from Q
• C. 2 cm from P
• D. 4 cm from P

Answer 1

The correct option is B 4 cm from Q

Given

Wire 1 have current i_{1}=5A

Wire 2 have current i_{2}=2A

Distance between them is d=6m

current flow in both wires is in opposite direction

Solution

Let x be the distance of a point from wire 2 from right where magnetic field is zero.

Magnetic field of wire on a point is $=\frac{{\mu }_0\ast 2i}{4\pi d}$

For wire 1

$B_1=\frac{{\mu }_0\ast 2i_1}{4\pi (d+x)}$

For wire 2

$B_2=\frac{{\mu }_0\ast 2i_2}{4\pi \left(x\right)}$

$B_1=B_2$

Therefore

$\frac{{\mu }_0\ast 2i_1}{4\pi (d+x)}=\frac{{\mu }_0\ast 2i_2}{4\pi \left(x\right)}$

Putting values

x=4

The correct option is B