Question

Two circular coils of radii $5\text{cm}$ and $10\text{cm}$ carry equal current of $2\text{A}$. The coils have $50$ and $100$ turns respectively and are placed in such a way that their planes as well as their centre coincide magnitude of magnetic field at the common centre of the coil is

• A. $8\pi \times {10}^{-4}\text{T},$ if current in the coils are in same sense
• B. $4\pi \times {10}^{-4}\text{T},$ if current in the coil are in opposite sense.
• C. zero, if current in the coils are in opposite sense
• D. $8\pi \times {10}^{-4}\text{T},$ if current in the coil are in opposite sense

Answer 1

Answer: (A), (C)

zero, if current in the coils are in opposite sense

Given:
$r_1=5\text{cm},$
$r_2=10\text{cm},$
$N_1=50$
$N_2=100$
$I_1=I_2=2\text{A}$
When current flows in same direction
$B_{\text{Net}}=\frac{N_1{\mu }_0{I}_1}{2\pi r_1}+\frac{{\mu }_0{N}_2{I}_2}{2\pi r_2}$
$\Rightarrow B_{\text{Net}}=\frac{{\mu }_0}{\pi }[\frac{N_1}{r_1}+\frac{N_2}{r_2}]=\frac{4\pi \times {10}^{-7}}{\pi }[\frac{50}{5\times {10}^{-2}}+\frac{100}{10\times {10}^{-2}}]=8\pi \times {10}^{-4}\text{T}$
When current flows in opposite direction
$B_{\text{Net}}=\frac{N_1{\mu }_0{I}_1}{2\pi r_1}-\frac{{\mu }_0{N}_2{I}_2}{2\pi r_2}=0$

$a,c$ are correct