[2013EM/HMW-07]

PHY 102: Introduction to Physics-2
Tutorial-7
(Magnetic field, Biot-savart’s and Ampere’s law)

1. Magnetic field using Biot-savart's law: A loop of wire has the shape of two concentric semicircles connected by two radial segments (Fig.1). The loop carries current $I$ as shown. Find the magnetic field at the point $P$ using the law of Biot-Savart. 
2. Magnetic field in a wire carrying a current density $J(r)$: A long copper wire of cross-sectional radius $R$ carries a current density $J(r)=Ae^{-Kr^\prime}$. Use Ampere's law to determine $B$ as a function of the distance $a$ from the centre of the wire. Sketch the result. the integral identity $\int e^{-ax}xdx=-(x/a)e^{-ax}+e^{-ax}/a+C$ may be of use.
3. Magnetic field in a co-axial cable. A coaxial cable consists of a long cylindrical copper wire of radius $r_1$ surrounded by a cylindrical insulating shell of outer radius $r_2$. A final conducting cylindrical shell of outer radius $r_3$ surrounds the insulating shell. The wire and conducting shell carry equal but opposite currents $I$ uniformly distributed over their volumes. Find formulas for the magnetic field in each of the regions $0<a<r_1$, $r_1<a<r_2$, $r_2<a<r_3$, and $a=>r_3$, where $a$ is the radial distance from the center of the cable. Sketch the result.