Question

Two identical, flat, circular coils of wire each have $100$ turns and a radius of $0.4\text{m}$. The coils are arranged coaxially, one beside the other, with their planes parallel and with separation $0.6\text{m}$. Each coil carries a current of $10\text{A}$ as shown. Determine the magnitude of the magnetic field at a point on the common axis of the coils and midway between them.

• A. $2.016\times {10}^{-3}\text{T}$
• B. $2.016\times {10}^{-7}\text{T}$
• C. $1.6\times {10}^{-3}\text{T}$
• D. $1.6\times {10}^{-5}\text{T}$

Answer 1

The correct option is C $1.6\times {10}^{-3}\text{T}$

For a point midway between the coils,

$R=0.4\text{m}$ and $x=0.3\text{m}$

The net magnetic field at the midpoint,

$B=\frac{{\mu }_{o}NI{R}^2}{2(R^2+x^2{)}^{3/2}}+\frac{{\mu }_{o}NI{R}^2}{2(R^2+x^2{)}^{3/2}}$

$=\frac{{\mu }_{o}NI{R}^2}{(R^2+x^2{)}^{3/2}}$

Substituting the values,

$B=\frac{4\pi \times {10}^{-7}\times 100\times 10\times {0.4}^2}{({0.4}^2+{0.3}^2{)}^{3/2}}$

$=1.6\times {10}^{-3}\text{T}$

Hence, option $\left(C\right)$ is the correct answer.