diff --git a/_psets/04.md b/_psets/04.md index a9fc33c6fbfa0d1335d90cf802527e19aafd9f15..ea8216bc15b22138cdb837114cd3500706797414 100644 --- a/_psets/04.md +++ b/_psets/04.md @@ -199,11 +199,11 @@ equal to $$\num{2e-7}$$ newton per metre of length." Show that that current at that distance produces that force. First let's find the magnetic field of an infinitely long straight conductor. Let's use a -cylindrical coordinate system along this axis. Considering the Biot-Savart Law and the symmetry of -this problem, the magnetic field must be oriented along $$\hat{\mathrm{d} \theta}$$, with a -magnitude that depends only on $$r$$. Consider then a circle of radius $$r$$ centered on the wire. -Ampère's Law tells us that the magnitude of the field at any point on this circle is $$I / (2 -\pi r)$$. +cylindrical coordinate system along this axis. Considering the [Biot-Savart +Law](https://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law) and the symmetry of this problem, the +magnetic field must be oriented along $$\hat{\mathrm{d} \theta}$$, with a magnitude that depends +only on $$r$$. Consider then a circle of radius $$r$$ centered on the wire. Ampère's Law +tells us that the magnitude of the field at any point on this circle is $$I / (2 \pi r)$$. The differential force exerted by this field on a differential piece of current is $$dF = I (dl \times B)$$. In this case the direction of the current and the magnetic field are perpendicular, so diff --git a/_psets/10.md b/_psets/10.md index 2377759c71d9e3920003cec0533c942aa4116d40..5e2c544cfb9d8b9f9b663439fb1e0a01d38419e2 100644 --- a/_psets/10.md +++ b/_psets/10.md @@ -136,5 +136,18 @@ coercivity of iron is $$\num{4e3} \si{A/m}$$. ## (13.6) {:.question} -Approximately what current would be required in a straight wire to be able to erase a $$\gamma \text{-} Fe_2 O_3$$ -recording at a distance of 1 cm? +Approximately what current would be required in a straight wire to be able to erase a $$\gamma +\text{-} Fe_2 O_3$$ recording at a distance of 1 cm? + +As found in problem 6.4 in [problem set 4](/psets/04.html), the magnitude of the magnetic field a +distance $$r$$ away from an infinitely long and thin conductor carrying a current $$I$$ is $$I/(2 +\pi r)$$. To erase information stored on $$Fe_2 O_3$$ we need this field to be about as strong as +the coercivity $$H_C = 300 \si{Oe}$$. Thus the current needed is + +$$ +\begin{align*} +I &= 2 \pi r H_C \\ +&= 2 \pi \cdot 10^{-2} \si{m} \cdot 300 \si{Oe} \cdot \frac{79.6 \si{A/m}}{1 \si{Oe}} \\ +&= 1500 \si{A} +\end{align*} +$$