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Magnetisation

A wire loop P...

Question

A wire loop PQRSP is constructed by joining two semi-circular coils of radius $r_{1}$ and $r_{2}$ respectively, as shown in the figure. If the current flowing in the loop is I, then the magnetic induction at the point O is:

\frac{μ_{0} I}{4} [\frac{1}{r_{1}} - \frac{1}{r_{2}}]

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\frac{μ_{0} I}{4} [\frac{1}{r_{1}} + \frac{1}{r_{2}}]

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\frac{μ_{0} I}{2} [\frac{1}{r_{1}} - \frac{1}{r_{2}}]

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\frac{μ_{0} I}{2} [\frac{1}{r_{1}} + \frac{1}{r_{2}}]

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Solution

The correct option is A $\frac{μ_{0} I}{4} [\frac{1}{r_{1}} - \frac{1}{r_{2}}]$

Magnetic field due to coil of radii $r_{1}$
$_{1} = \frac{1}{2} \times \frac{μ_{0} I}{2 r_{1}}$ out of plane
Magnetic field due to coil of radii $r_{2}$
$_{2} = \frac{1}{2} \times \frac{μ_{0} I}{2 r_{2}} \otimes$ in of plane
$B \propto \frac{1}{r}$ hence $_{n e t} = \frac{μ_{0} I}{4 r_{1}} - \frac{μ_{0} I}{4 r_{2}}$
$\Rightarrow \frac{μ_{0} I}{4} (\frac{1}{r_{1}} - \frac{1}{r_{2}})$

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A wire loop PQRSP is constructed by joining two semi-circular coils of radius r1 and r2 respectively, as shown in the figure. If the current flowing in the loop is I, then the magnetic induction at the point O is:

The correct option is A μ0I4[1r1−1r2] Magnetic field due to coil of radii r1 →B1=12×μ0I2r1 out of plane Magnetic field due to coil of radii r2 →B2=12×μ0I2r2⊗ in of plane B∝1r hence →Bnet=μ0I4r1−μ0I4r2 ⇒μ0I4(1r1−1r2)

A wire loop PQRSP is constructed by joining two semi-circular coils of radius $r_{1}$ and $r_{2}$ respectively, as shown in the figure. If the current flowing in the loop is I, then the magnetic induction at the point O is: