2016-14.md

course	course_year	question_number	tags	title	year
Electromagnetism	IB	14	IB 2016 Electromagnetism	Paper 2, Section I, $6 \mathrm{D}$	2016

(a) Derive the integral form of Ampère's law from the differential form of Maxwell's equations with a time-independent magnetic field, $\rho=0$ and $\mathbf{E}=\mathbf{0}$.

(b) Consider two perfectly-conducting concentric thin cylindrical shells of infinite length with axes along the $z$-axis and radii $a$ and $b(a<b)$. Current $I$ flows in the positive $z$-direction in each shell. Use Ampère's law to calculate the magnetic field in the three regions: (i) $r<a$, (ii) $a<r<b$ and (iii) $r>b$, where $r=\sqrt{x^{2}+y^{2}}$.

(c) If current $I$ now flows in the positive $z$-direction in the inner shell and in the negative $z$-direction in the outer shell, calculate the magnetic field in the same three regions.