Question

Two long straight wires carrying current of $5\text{A}$ each. Find the point for which magnetic field is zero

• A. $A$
• B. $B$
• C. $C$
• D. $D$

Answer 1

Answer: (A), (D)

$D$

As all points are equidistant from both the wires and both wires carry same current, the magnetic field at all point $\text{A, B, C}$ and $\text{D}$ due to both the wires will be equal in magnitude.

Magnetic field due to Wire-$1$ and $2$:

$\left|\overrightarrow{B_1}\right|=\frac{{\mu }_{0}I}{2\pi a}$

$\left|\overrightarrow{B_2}\right|=\frac{{\mu }_{0}I}{2\pi a}$

Using the "Fleming's right-hand thumb rule" the directions magnetic field due to the wire-$1$ and $2$ are shown at all the points as shown in the figure.


From the figure, the magnetic field at points $A$ and $D$ are

$B_A=B_D=B_1-B_2=0[\because B_1=B_2]$

The magnetic fields at points $B$ and $C$ are,

$B_B=B_1+B_2=2\times \frac{{\mu }_{0}I}{2\pi a}=\frac{{\mu }_{0}I}{\pi a}\left[\text{Outwards}\right(\odot \left)\right]$

$B_C=B_1+B_2=2\times \frac{{\mu }_{0}I}{2\pi a}=\frac{{\mu }_{0}I}{\pi a}\left[\text{Inwards}\right(\otimes \left)\right]$

Hence, options $\left(a\right)$ and $\left(d\right)$ are the correct answers. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->