(Solved): Figure: A toriod with a square cross-section. The figure on the left shows the toroid with inner r ...

Figure: A toriod with a square cross-section. The figure on the left shows the toroid with inner radius $R$ and outer radius $R+a$. A current $I$ flows up the screen and over the top of the toroid on the loop lowest on the screen. This is the view from on top. The figure on the right shows the length and height of a cross section of the toroid, which is $a$. This is what you would see if you sliced through part of the toroid. A toroid consisting of $N=316$ loops with a square cross-section and side lengths $a=3.36\mathrm{cm}$ and inner radius $R=23.6\mathrm{cm}$ has a current $I=4.50\mathrm{A}$ flowing through it in the direction shown in the figure. Part 1) Write an expression for the magnetic field strength a distance $r\mathrm{cm}$ from the centre of the toriod where $R<r<R+a$. Your expression should only contain the variable $r$, evaluate all other variables and constants. $\vec{B}=$ $\mathrm{T}$ in the direction when looking from on top (as in the left hand figure). Your last answer was interpreted as follows: $\frac{2.844?10^{?4}}{r}$ The variables found in your answer were: $[r]$ Your last answer was interpreted as follows: $\frac{2.844?10^{?4}}{r}$ The variables found in your answer were: $[r]$ Part 2) Calculate the magnitude of the magnetic flux through the square cross-section of the toroid. $?{?}_B?=$ Part 3) Which of the following statements are true? If the magnetic flux through the square cross-section was changing, there would be an induced electric field. Once the current has been flowing for a while, the induced magnetic field will decrease the magnetic field inside the toroid. When the current is first switched on, there is an induced magnetic field in the toroid in an anticlockwise direction when looking from on top, as shown in the figure. Immediately after the current is switched off, there is an induced magnetic field in the toroid in an anticlockwise direction when looking from on top, as shown in the figure. The Biot-Savart law could be used to calculate the magnetic field inside the toroid but it would be harder than using Ampere's law.