Question

Point A in FIGURE EX29.15 is $2.0\mathrm{mm}$from the wire. What is the magnetic field strength at point A? You can assume that the wire is very long and that all other wires are too far away to contribute to the magnetic field.

Short answer

The magnetic field strength at point A is$B_A=0.12\mathrm{mT}$.

Step-by-step solution

Given Information 

We have given,

A circuit diagram as shown in the figure.

We have to find the magnetic field at point A.

Simplify

The determine the magnetic field at point A, We have to find the magnetic field ion the wire.

The equivalent resistance for series combination is calculated by

$R_{eq\mathit{1}}=20\Omega +30\Omega =50\Omega$

then current will be,

$I=\frac{\epsilon }{R_{eq}}=\frac{60V}{50\Omega }=1.2A$

then the magnetic field at a point a will be

$$\begin{gathered} B_A=\frac{{\mu }_o}{2\pi }\frac{I}{r} \\ =\frac{\left(4\pi \times {10}^{-7}T·m/A\right)\left(1.2A\right)}{2\pi \left(2\times {10}^{-3}m\right)} \\ =0.12\times {10}^{-3}T \\ =0.12\mathrm{mT} \end{gathered}$$