Question

what is the magnitude of the magnet field 1.5cm from a long, straight conductor carrying a current of 3.2A? what is the magnitude of the magnet field 1.5cm from a long, straight conductor carrying a current of 3.2A? @Physics

Answer 1

Recall Ampère's Law for constant electric fields:\[\oint\limits_C \vec B \cdot d\vec \ell = \mu_0I\]Here, C represents some curve we will integrate around. We will choose a circle of radius r that encloses a portion of the wire in a symmetric manner. Along the curve, the length elements will be parallel to the magnetic field so we can drop the vector notation.\[\oint Bd\ell = \mu_0 I\]Now, since we have chosen a symmetrical shape, we can drop the integral sign and make the differential an actual variable.
\[B\ell = \mu_0I \Rightarrow B = \frac{\mu_0 I}{\ell}\]The circumference of our circle is 2(pi)r, so therefore our answer is as follows.\[\boxed{\displaystyle B = \frac{\mu_0 I}{2\pi r}}\]The direction of the magnetic field is given by the right-hand rule.