solenoid

[logistic_guy]

A \(\displaystyle 40.0\)-\(\displaystyle \text{cm}\) long solenoid \(\displaystyle 1.35 \ \text{cm}\) in diameter is to produce a field of \(\displaystyle 0.385 \ \text{mT}\) at its center. How much current should the solenoid carry if it has \(\displaystyle 1000\) turns of wire?

 

[khansaheb]

A \(\displaystyle 40.0\)-\(\displaystyle \text{cm}\) long solenoid \(\displaystyle 1.35 \ \text{cm}\) in diameter is to produce a field of \(\displaystyle 0.385 \ \text{mT}\) at its center. How much current should the solenoid carry if it has \(\displaystyle 1000\) turns of wire?

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[logistic_guy]

The relation between magnetic field and current in the solenoid is:

\(\displaystyle B = \mu_0\frac{NI}{L}\)

\(\displaystyle 0.385 \times 10^{-3} = 4\pi \times 10^{-7}\frac{1000I}{0.4}\)

This gives:

\(\displaystyle I = \textcolor{blue}{0.123 \ \text{A}}\)