Question

A rod of length $2.4\, m$ and radius $4.6\, mm$ carries a negative charge of $4.2 \times 10^{-7}\, C$ spread uniformly over it surface. The electric field near the mid-point of the rod, at a point on its surface is

• A. $- 8.6 \times 10^5\, N\, C^{-1}$
• B. $ 8.6 \times 10^4\, N\, C^{-1}$
• C. $- 6.7 \times 10^5\, N\, C^{-1}$
• D. $ 6.7 \times 10^4\, N\, C^{-1}$

Answer 1

Answer: (C)

Here, $\quad 1=2.4 m , r =4.6 mm =4.6 \times 10^{-3} m$ $q =4.6 \times 10^{-7} C$
Linear charge density, $\quad \lambda=\frac{ q }{1}=\frac{-4.2 \times 10^{-7}}{2.4}=-1.75 \times 10^{-7} Cm ^{-1}$ Electric field,
$ E =\frac{\lambda}{2 \pi \varepsilon_{0} r }=\frac{-1.75 \times 10^{-7}}{2 \times 3.14 \times 8.854 \times 10^{-12} \times 4.6 \times 10^{-3}}=-6.67 \times 10^{5} NC ^{-1} $