Along straight wire carries a current $I=10\text{ A}$. A point $P$ is at a distance $r=5\text{ cm}$ from the wire. What is the magnitude of the magnetic field $B$ at point $P$?

Solution

1. Identify the given values: current $I=10\text{ A}$, distance $$\begin{array}{rl}r& =5\text{ cm}\\ & =0.05\text{ m}\end{array}$$, and the permeability of free space ${\mu }_0=4\pi \times 10^{-7}\text{ T}\cdot \text{m/A}$.
2. Use the formula for the magnetic field of along straight wire: $B=\frac{{\mu }_{0}I}{2\pi r}$.
3. Substitute the values into the equation: $B=\frac{(4\pi \times 10^{-7}\text{ T}\cdot \text{m/A})(10\text{ A})}{2\pi (0.05\text{ m})}$.
4. Simplify the expression to find $$\begin{array}{rl}B& =\frac{2\times 10^{-6}}{0.05}\\ & =4\times 10^{-5}\text{ T}\end{array}$$.
5. Hence the answer is (A).