Two circular coils P and Q of 100 turns each have same radius of πcm. 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 xmT, where x= ______. [Use μ0=4π×10−7TmA−1]
Answer: 20
Solution
The field at the centre of a circular coil of N turns carrying current i is B=2rμ0Ni, with r=π cm =π×10−2 m.
For coil P (i=1 A):
BP=2π×10−24π×10−7×100×1=2×10−3T=2mT
For coil Q (i=2 A):
BQ=2π×10−24π×10−7×100×2=4×10−3T=4mT
Since the coil planes are mutually perpendicular, BP and BQ are perpendicular vectors:
Bnet=BP2+BQ2=4+16=20mT
Hence x = 20
JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Integer answer
