Appeared in: 2025 (2 sets)
(b) (i) Current $I$ ($= 1\text{ A}$) is passing through a copper rod ($n = 8\cdot5 \times 10^{28}\text{ m}^{-3}$) of varying cross-sections as shown in the figure. The areas of cross-section at points A and B along its length are $1\cdot0 \times 10^{-7}\text{ m}^2$ and $2\cdot0 \times 10^{-7}\text{ m}^2$ respectively. Calculate :
(I) the ratio of electric fields at points A and B.
(II) the drift velocity of free electrons at point B.
(ii) Two point charges $q_1$ ($= 16\text{ }\mu\text{C}$) and $q_2$ ($= 1\text{ }\mu\text{C}$) are placed at points $\vec{r}_1 = (3\text{ m})\hat{i}$ and $\vec{r}_2 = (4\text{ m})\hat{j}$. Find the net electric field $\vec{E}$ at point $\vec{r} = (3\text{ m})\hat{i} + (4\text{ m})\hat{j}$.