### Magnetic Effects Of Current Question 15

#### Question 15 - 2024 (31 Jan Shift 2)

Two circular coils P and Q of 100 turns each have same radius of $\pi cm$. 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 $\sqrt{x m T}$, where $x=$

[Use $\mu _0=4 \pi \times 10^{-7} TmA^{-1}$ ]

## Show Answer

#### Answer: (20)

#### Solution:

$B _P=\frac{\mu _0 Ni _1}{2 r}=\frac{\mu _0 \times 1 \times 100}{2 \pi}=2 \times 10^{-3} T$

$B _Q=\frac{\mu _0 Ni _2}{2 r}=\frac{\mu _0 \times 2 \times 100}{2 \pi}=4 \times 10^{-3} T$

$B _{\text {net }}=\sqrt{B _P^{2}+B _Q^{2}}$

$=\sqrt{20} mT$

$x=20$