Magnetic field due to current in a straight wire A long
Chapter 4, Problem 72E(choose chapter or problem)
Magnetic field due to current in a straight wire A long straight wire of length 2L on the y-axis carries a current I. According to the Biot-Savart Law, the magnitude of the magnetic field due to the current at a point (a, 0) is given by
\(B(a)=\frac{\mu_{0} I}{4 \pi} \int_{-L}^{L} \frac{\sin \theta}{r^{2}} d y\)
where \(\mu_{0}\) is a physical constant, a>0, and \(\theta\), r, and y are related as shown in the figure.
(a) Show that the magnitude of the magnetic field at (a, 0) is \(B(a)=\frac{\mu_{0} I L}{2 \pi a \sqrt{a^{2}+L^{2}}}\).
(b) What is the magnitude of the magnetic field at (a, 0) due to an infinitely long wire \((L \rightarrow \infty)\)?
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