Two circular coils P and Q of 100 turns each have same radius of π cm . The currents in P and R are 1 A and 2 A respectively. P and Q are placed with their planes mutually perpendicular with their cen

Question

Two circular coils P and Q of 100 turns each have same radius of π cm . The currents in P and R are 1 A and 2 A 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 x mT , where x = ______. [Use μ 0 = 4 π × 10 − 7 T m A − 1 ]

TestHub · Accepted Answer

Consider two coils as shown below:

Magnetic field due to P, $B_{P} = N (\frac{μ_{0} i_{1}}{2 r}) = 100 \times \frac{μ_{0} \times 1}{2 (π \times 10^{- 2})} = 2 \times 10^{- 3} T$

Magnetic field due to Q,

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

Therefore, $B_{net} = \sqrt{B_{P}^{2} + B_{Q}^{2}}$

$= \sqrt{20} mT$

Hence, $x = 20$

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