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NEET Sample Paper NEET Sample Test Paper-57

  • question_answer
    Two similar coil of radius R are lying concentrically with their planes at right angles to each other. The currents flowing in them are I and 21, respectively. The resultant magnetic field induction at the centre will be:

    A) \[\frac{\sqrt{5}{{\mu }_{0}}I}{2R}\]                 

    B) \[\frac{3{{\mu }_{0}}I}{2R}\]

    C) \[\frac{{{\mu }_{0}}I}{2R}\]                             

    D) \[\frac{{{\mu }_{0}}I}{R}\]

    Correct Answer: A

    Solution :

    [a] \[{{\vec{B}}_{1}}=\frac{{{\mu }_{{}^\circ }}I}{2R}\,\,{{\vec{B}}_{2}}=\frac{2{{\mu }_{{}^\circ }}I}{2R}=\frac{{{\mu }_{{}^\circ }}I}{R}\] \[\vec{B}_{net}^{2}=\vec{B}_{1}^{2}+\vec{B}_{2}^{2}\] \[={{\left[ \frac{{{\mu }_{{}^\circ }}I}{2R} \right]}^{2}}+{{\left[ \frac{{{\mu }_{{}^\circ }}I}{R} \right]}^{2}}\] \[\frac{\mu _{{}^\circ }^{2}{{I}^{2}}}{4{{R}^{2}}}+\frac{\mu _{{}^\circ }^{2}{{I}^{2}}}{{{R}^{2}}}\] \[\frac{\mu _{{}^\circ }^{2}{{I}^{2}}}{{{R}^{2}}}\,\left[ \frac{1}{4}+1 \right]\] \[\vec{B}_{net}^{2}\frac{5}{4}\,{{\left[ \frac{\mu _{{}^\circ }^{{}}I}{R} \right]}^{2}}\] \[\vec{B}_{net}^{{}}\frac{\sqrt{5}}{4}\,\frac{\mu _{{}^\circ }^{{}}I}{R}\]


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