A) \[3:4\]
B) \[5:3\]
C) \[7:11\]
D) \[11:7\]
Correct Answer: B
Solution :
When the current in the wires is in same direction. Magnetic field at mid-point \[O\] due to \[I\] and \[II\] wires are respectively \[{{B}_{I}}=\frac{{{\mu }_{o}}}{4\pi }\frac{2{{i}_{1}}}{x}\otimes \] and \[{{B}_{II}}=\frac{{{\mu }_{0}}}{4\pi }\frac{2{{i}_{2}}}{x}\varnothing \] So, the net magnetic field at\[O\] \[{{B}_{net}}=\frac{{{\mu }_{0}}}{4\pi }\times \frac{2}{x}\times ({{i}_{1}}-{{i}_{2}})\] \[\Rightarrow \] \[10\times {{10}^{-6}}=\frac{{{\mu }_{0}}}{4\pi }\cdot \frac{2}{x}({{i}_{1}}-{{i}_{2}})\] ... (i) when the direction of \[{{i}_{2}}\] is reversed \[{{B}_{I}}=\frac{{{\mu }_{0}}}{4\pi }\cdot \frac{2{{i}_{1}}}{x}\otimes \] and \[{{B}_{II}}=\frac{{{\mu }_{0}}}{4\pi }\cdot \frac{2{{i}_{2}}}{x}\otimes \] So, net magnetic field at \[O\] \[{{B}_{net}}=\frac{{{\mu }_{0}}}{4\pi }\times \frac{2}{x}\times ({{i}_{1}}+{{i}_{2}})\] \[\Rightarrow \] \[40\times {{10}^{-6}}=\frac{{{\mu }_{0}}}{4\pi }\cdot \frac{2}{x}({{i}_{1}}+{{i}_{2}})\] ... (ii) Dividing Eq. (ii) by Eq. (i), we get \[\frac{{{i}_{1}}+{{i}_{2}}}{{{i}_{1}}-{{i}_{2}}}=\frac{4}{1}\] \[\Rightarrow \] \[\frac{{{i}_{1}}}{{{i}_{2}}}=\frac{5}{3}\]You need to login to perform this action.
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