Question

A pair of long, straight current-carrying wires and four marked points are shown in above figure. Find out the points at which net magnetic field is zero?

• A. Point 1 only
• B. Points 1 and 2 only
• C. Point 2 only
• D. Points 3 and 4 only
• E. Point 3 only

Answer 1

Answer: (A)

Point 1 only

Magnetic field at a point at a distance $d$ from a current carrying wire is $\frac{{\mu }_{0}I}{2\pi d}$

Thus $B\propto \frac{I}{d}$

At point 1,

Magnetic field due to wire with current $I=\frac{{\mu }_{0}I}{2\pi \left(3a\right)}$ out of the plane

Magnetic field due to wire with current $2I=\frac{{\mu }_0\left(2I\right)}{2\pi \left(6a\right)}=\frac{{\mu }_{0}I}{2\pi \left(3a\right)}$ into the plane

Thus net magnetic field at point 1 is zero.