KCET · Physics · Magnetic Effects of Current
In the diagram, \(I_{1}, I_{2}\) are the strength of the currents in the loop and straight conductors respectively. \(O A=A B=R\). The net magnetic field at the centre \(O\) is zero. Then the ratio of the currents in the loop and the straight conductos is
- A \(\pi\)
- B \(2 \pi\)
- C \(\frac{1}{\pi}\)
- D \(\frac{1}{2 \pi}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2 \pi}\)
Step-by-step Solution
Detailed explanation
Given that the net magnetic field at the centre \(O\) is zero. Therefore, magnetic field at \(O\) due to circular coil and straight conductor must be equal and opposite in direction.
\(\therefore \frac{\mu_{0} l_{1}}{2 R}=\frac{\mu_{0} I_{2}}{2 \pi(2 R)} \Rightarrow \frac{I_{1}}{I_{2}}=\frac{1}{2 \pi}\)
\(\therefore \frac{\mu_{0} l_{1}}{2 R}=\frac{\mu_{0} I_{2}}{2 \pi(2 R)} \Rightarrow \frac{I_{1}}{I_{2}}=\frac{1}{2 \pi}\)
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