Answer to Question #289837 in Electric Circuits for boshra

Question

 Find the current in a long, straight wire needed to develop a magnetic field of    

       5x10-7 T at 6m from the wire.

Answer 1

We shall find the current which is needed to develop the magnetic field of $5$ X $10^{-7}T$

From the question, we have the parameters

$B=5$ X $10^{-7}T$

length, $x=6m$

Current, $I=?$

Now,

Using the formula

$\displaystyle B=\frac{\mu_{o} I}{2\pi x}$

We shall make $I$ the subject of the equation

We have

$\displaystyle I=\frac{2\pi x B}{\mu_{o}}$

where $\mu_{o}=4\pi \times 10^{-7}$

Substituting into the formula, we have

$\displaystyle I=\frac{2\pi \times 6\times 5\times10^{-7}}{4\pi \times 10^{-7}}$

$\displaystyle I=\frac{1 \times 30\times10^{-7}}{2 \times 10^{-7}}$

$\displaystyle I=\frac{30\times10^{-7}}{2 \times 10^{-7}}$

$\displaystyle I=\frac{30}{2}$

$I=15A$

which is the needed current to develop the magnetic field of $5\times10^{-7}T$