Respuesta :
Answer:
Magnetic field shall be zero at exactly in between the wires.
Explanation:
We can find the magnetic field by biot Savart law as follows
[tex]\overrightarrow{dB}=\frac{\mu _{0}I}{4\pi }\int \frac{\overrightarrow{dl}\times \widehat{r}}{r^{2}}[/tex]
For current carrying wire in positive y direction we have
[tex]\overrightarrow{dB_{1}}=\frac{\mu _{0}Idl}{4\pi }\int \frac{\widehat{j}\times \widehat{r_{1}}}{r_{1}^{2}}[/tex]
Similarly for wire carrying current in -y direction we have [tex]\overrightarrow{dB_{2}}=\frac{-\mu _{0}Idl}{4\pi }\int \frac{\widehat{j}\times \widehat{r_{2}}}{r_{2}^{2}}[/tex]
Thus the net magnetic field at any point in space is given by
[tex]\overrightarrow{dB_{1}}+\overrightarrow{dB_{2}}[/tex]
[tex]\frac{\mu _{0}Idl}{4\pi }\int \frac{\widehat{j}\times \widehat{r_{1}}}{r_{1}^{2}}+\frac{-\mu _{0}Idl}{4\pi }\int \frac{\widehat{j}\times \widehat{r_{2}}}{r_{2}^{2}}=0\\\\\Rightarrow \overrightarrow{r_{1}}=\overrightarrow{r_{2}}[/tex]
For points with same position vectors from the 2 wires we have a net zero magnetic field. These points are exactly midway between the 2 wires
