Two similar coils of radius r are lying concentrically with their planes at right angles to each others. The currents flowing in them are I \ and\ 2 I, respectively. The resultant magnetic field induction at  the centre will be:

  • Option 1)

    \frac{\sqrt{5}\mu_{o}I}{2R}

  • Option 2)

    \frac{{3}\mu_{o}I}{2R}

  • Option 3)

    \frac{\mu_{o}I}{2R}

  • Option 4)

    \frac{\mu_{o}I}{R}

 

Answers (1)

 

Magnetic field due to cCrcular Current Carrying arc -

B=frac{mu_{o}}{4pi}:frac{2pi i}{r}=frac{mu_{o}i}{2r}

- wherein

 

 B_{1}=\frac{\mu _{oI}}{2r } \:\:\:\:\:B=\sqrt{B_{1}^{2}+B_{2}^{2}}=\sqrt{5}\frac{\mu ^oI}{2r}\\ B_{2}=\frac{\mu_{o}.2I}{2r}


Option 1)

\frac{\sqrt{5}\mu_{o}I}{2R}

This option is correct 

Option 2)

\frac{{3}\mu_{o}I}{2R}

This option is incorrect 

Option 3)

\frac{\mu_{o}I}{2R}

This option is incorrect 

Option 4)

\frac{\mu_{o}I}{R}

This option is incorrect 

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