SECTION B [10Marks]
ANSWER ONLY ONE (1) QUESTION IN THIS SECTION
Question 1
A. Point charges of \( 1 \mathrm{nC} \) and \( -2 \mathrm{nC} \) are located at \( (0,0,0) \) and \( (1,1,1) \), respectively, in free space. Determine the vector force acting on each charge.
B. A \( 2-\mu \mathrm{C} \) point charge is in free space at \( \mathrm{A}(4,3,5) \). Find \( E_{\rho}, E_{\varphi} \), and \( E_{z} \) at \( P(8,12,2) \)
Question 2
A. Let a point charge \( Q_{1}=25 \mathrm{nC} \) be located at \( \mathrm{P}_{1}(4,-2,7) \) and a charge \( \mathrm{Q} 2=60 \mathrm{nC} \) be at \( \mathrm{P} 2(-3,4,-2) \).
(a) If \( \varepsilon=\varepsilon 0 \), find \( \mathrm{E} \) at \( \mathrm{P} 3(1,2,3) \).
(b) At what point on the \( y \)-axis is \( \mathrm{Ex}_{\mathrm{x}}=0 \) ?
B. A uniform volume charge density of \( 0.2 \mu \mathrm{C} / \mathrm{m}^{3} \) is present throughout the spherical shell, extending from \( r=3 \mathrm{~cm} \) to \( r=5 \mathrm{~cm} \). If \( \rho v=0 \) elsewhere, find
(a) the total charge present throughout the shell and
(b) \( r 1 \) if half the total charge is located in the region \( 3 \mathrm{~cm}<r<r 1 \).
