Two circular coils P and Q of 100 turns each have same radius of cm. The currents in P and R are 1A and 2A respectively. P and Q are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at th

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Solution

Q.
Two circular coils P and Q of 100 turns each have same radius of $π$ cm. The currents in P and R are 1A and 2A respectively. P and Q are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $\sqrt{x} m T,$ where $x =$ ____ .

$[Use μ_{0} = 4 π \times 10^{- 7} {TmA}^{- 1}]$ [2024]

Ans.
(20)

$B_{P} = \frac{μ_{0} N i_{1}}{2 r} = \frac{μ_{0} \times 1 \times 100}{2 π} = 2 \times 10^{- 3} T$

$B_{Q} = \frac{μ_{0} N i_{2}}{2 r} = \frac{μ_{0} \times 2 \times 100}{2 π} = 4 \times 10^{- 3} T$

$B_{net} = \sqrt{B_{P}^{2} + B_{Q}^{2}} = \sqrt{20} mT$

$x = 20$

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