Question

Two infinitely long wires $P$ and $Q$ separated by a distance of $10cm$ in air, carry currents $I$ and $2I$ in opposite directions as shown in the figure. The resultant magnetic field due to currents in these wires will be zero at :

• A. Point $A$
• B. Point $B$
• C. Point $C$
• D. None of the points $A,B,C$

Answer 1

The correct option is A Point $A$

Magnetic field at a distance $d$ due to a straight wire, $B=\frac{{\mu }_{o}I}{2\pi d}$

Magnetic field at point A due to wire P, $B_1=\frac{{\mu }_o{I}_1}{2\pi d_1}=\frac{{\mu }_{o}I}{2\pi \left(.10\right)}=\frac{{\mu }_{o}I}{0.2\pi }$ (out of page)

Magnetic field at point A due to wire Q, $B_2=\frac{{\mu }_o{I}_2}{2\pi d_2}=\frac{{\mu }_o\left(2I\right)}{2\pi \left(.20\right)}=\frac{{\mu }_{o}I}{0.2\pi }$ (into the page)

Thus, total magnetic field at point A is zero as $B_1=B_2$ but in opposite direction.