Question

Two long parallel wires $\text{P}$ and $\text{Q}$ placed at a separation of $6\text{cm}$ carries electric currents, $I_1=5\text{A}$ and $I_2=2\text{A}$ respectively in the opposite directions as shown in the figure. Find the point on the line $\text{AB}$ where the resultant magnetic field is zero.

• A. $4\text{cm}$ away from $B$ and $10\text{cm}$ away from $A$
• B. $4\text{cm}$ away from $B$ and $2\text{cm}$ away from $A$
• C. At the midpoint of $AB$
• D. None of these

Answer 1

The correct option is A $4\text{cm}$ away from $B$ and $10\text{cm}$ away from $A$

On using the Right-hand thumb rule, we can see that magnetic fields due to both the current carrying wires are in the same direction at points between the wires, and in opposite directions at the points above wire $P$ and below wire $Q$.
Therefore, net magnetic field may be zero at points $C$ or $D$.


At $C$,

$\frac{{\mu }_o{I}_1}{2\pi x}=\frac{{\mu }_o{I}_2}{2\pi (0.06+x)}$

$\Rightarrow \frac{5}{x}=\frac{2}{0.06+x}$

$\Rightarrow x=$ Negative

$\Rightarrow$Not possible at $C$

At $D$,

$\frac{{\mu }_o{I}_1}{2\pi (0.06+y)}=\frac{{\mu }_o{I}_2}{2\pi y}$

$\Rightarrow \frac{5}{0.06+y}=\frac{2}{y}$

$\Rightarrow y=0.04\text{m}=4\text{cm}$

Therefore, net magnetic field is zero at $4\text{cm}$ away from $B$ and $10\text{cm}$ away from $A$.