Two identical long current carrying wires are bent into the shapes shown in the following figures

Question

Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centers P and Q of a semicircular arc are $B_{1}$ and $B_{2}$ respectively, then the ratio $\frac{B_{1}}{B_{2}}$ is ______. [2026]

Smart Achievers · Accepted Answer

(1)

$B_{P} = \frac{μ_{0} i}{4 π r} \times 2 + \frac{μ_{0} i}{4 r} = \frac{μ_{0} i}{4 r} (1 + \frac{2}{π})$

$B_{Q} = \frac{μ_{0} i}{4 π r} + \frac{μ_{0} i}{4 r} = \frac{μ_{0} i}{4 r} (1 + \frac{1}{π})$

$\Rightarrow \frac{B_{P}}{B_{Q}} = \frac{1 + 2 / π}{1 + 1 / π} = \frac{π + 2}{π + 1}$

Solution

Q.
Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centers P and Q of a semicircular arc are $B_{1}$ and $B_{2}$ respectively, then the ratio $\frac{B_{1}}{B_{2}}$ is ______. [2026]

1 $\frac{2 + π}{1 + π}$

2 $\frac{1 + π}{1 - π}$

3 $\frac{2 + π}{1 - π}$

4 $\frac{1 + π}{2 - π}$

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Solution

Q. Two identical long current carrying wires are bent into the shapes shown in the following figures. If the magnitude of magnetic fields at the centers P and Q of a semicircular arc are B1 and B2 respectively, then the ratio B1B2 is ______. [2026]

1 2+π1+π

2 1+π1-π

3 2+π1-π

4 1+π2-π