(Solved): (a) Define Biot-Savart's and Ampere's Circuital Law in magnetostatic. With the aid of appropriate d ...

(a) Define Biot-Savart's and Ampere's Circuital Law in magnetostatic. With the aid of appropriate diagram and symbols, compare both laws for the case of volume current element. (5 marks) (b) A rectangular current tube has side $A$ and $C$, parallel to $yz$-plane and lies between $?a/2$ to $a/2$, and side $B$ and $D$, parallel to $xz$-plane and lies between $?b/2$ to $b/2$, as shown in Figure Q.1(b). The center of each axis is located at the middle of the rectangular tube. Current, $I$ flow clockwise direction via sides $A?B?C?D?A$. Use suitable law and appropriate assumption to solve the following: (i) State the suitable law that can be applied with justification if, the length of $a$ and $b$ are much greater than $L(a>>L$ and $b>>)$ where $a=0.9b$. Sketch suitable diagram to support your answer. (4 marks) (ii) Based on Q.1(b)(i), determine total magnetic field intensity at the origin in term of $a$ and $b$. (6 marks) (iii) State the suitable law that can be applied with justification if, the length of $L$ and $b$ are much greater than $a(L?>a$ and $b>>a)$. Sketch a suitable diagram and give reason to support your answer. (4 marks) (iv) Based on Q.1(b)(iii), determine magnetic field intensity along z-axis for each of related sides if given the value of current density, ${\stackrel{?}{J}}_S=\frac{I}{5}(?\hat{x})\mathrm{A}/\mathrm{m}$ for side $\mathrm{B}$ and, ${\stackrel{?}{J}}_S=\frac{I}{5}(\hat{x})\mathrm{A}/\mathrm{m}$ for side $\mathrm{D}$. Then, find the total magnetic field of the related sides. (6 marks) Figure Q.1(b)