WBJEE · Physics · Magnetic Effects of Current
A circular loop of radius \(r\) of conducting wire connected with a voltage source of zero internal resistance produces a magnetic field
\(B\) at its centre. If instead, a circular loep of radius \(2 r,\) made of same material, having the same cross-section is connected to the same voltage source, what will be the magnetic ficld at its centre?
- A \(\frac{B}{2}\)
- B \(\frac{B}{4}\)
- C \(2B\)
- D \(B\)
Answer & Solution
Correct Answer
(B) \(\frac{B}{4}\)
Step-by-step Solution
Detailed explanation
\[ B=\frac{\mu_{0}}{2} \cdot \frac{I}{r} \] \(\because\) \[ I_{1}=\frac{V}{R_{1}} \] Case (I) \(l_{1}=2 \pi r\) (length of the loop). \[ R_{1}=\rho \frac{l_{1}}{A} \text { and } B_{1}=\frac{\mu_{0}}{2} \cdot \frac{I_{1}}{r} \] Case (II) \(I_{2}=2 \pi \cdot 2 r=2 l_{1}\)…
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