question_answer

Two concentric coils each of radius equal to\[2\pi \]cm are placed at right angles to each other. 3 A and 4 A are the currents flowing in each coil respectively. The magnetic induction in \[Wb/{{m}^{2}}\]at the centre   of   the   coils , will   be \[({{\mu }_{0}}=4\pi \times {{10}^{-7}}Wb/Am)\]            [AIEEE 2005]

A) \[12\times {{10}^{-5}}\]

B) \[{{10}^{-5}}\]

C) \[5\times {{10}^{-5}}\]

D) \[7\times {{10}^{-5}}\]

Correct Answer: C

Solution :

[c] The magnetic field induction at centre O due to circular current,

\[{{B}_{P}}\,=\frac{{{\mu }_{0}}}{2}\,\frac{{{l}_{2}}}{R}\,=\frac{4\pi \times {{10}^{-7}}\times 4}{2\times 0.02\,\pi }\,\]

and magnetic field induction at the centre due to circular current ,

Net magnetic field induction it the centre due to both the circular currentsand