Question

Two concentric coils, each of radius equal to $2\pi \text{cm}$, are placed at right angles to each other. Currents of $3\text{A}$ and $4\text{A}$, respectively, are flowing through the two coils. The magnetic induction, in $\text{Wb}{\text{m}}^{-2}$, at the center of the coils will be
$[{\mu }_0=4\pi \times {10}^{-7}\text{Wb}$ $\left({Am}^{-1}\right)]$

• A. $5\times {10}^{-5}$
• B. $7\times {10}^{-5}$
• C. $12\times {10}^{-5}$
• D. $\times {10}^{-5}$

Answer 1

Answer: (A)

$5\times {10}^{-5}$

$B_x=\frac{{\mu }_{0}i}{2r}=\frac{{\mu }_0\times 3}{2\times 2\pi \times {10}^{-2}}$

$B_y=\frac{{\mu }_{0}i}{2r}=\frac{{\mu }_0\times 4}{2\times 2\pi \times {10}^{-2}}$
$B_{net}=\frac{{\mu }_0}{4\pi }\sqrt{B_x^2+B_y^2}={10}^{-7}\times {10}^2\times \sqrt{3^2+4^2}$
$=5\times {10}^2\times {10}^{-7}=5\times {10}^{-5}T$
$=5\times {10}^{-5}Wb/m^2$