Question

s A horizontal insulating rod of length 11.0-cm and charge 19 nC is in a plane with a long straight vertical uniform line charge. The linear charge density of the long line charge is 3.9x10-7 c/m. What is the electric force on the rod if the end closest to the line charge is 2.0 cm away?

Answer 1

Answer:

F = 2.26 ×  10⁻³ N

Explanation:

given,

length of rod = 11 cm

charge  = 19 nC

linear charge density = 3.9 x 10⁻⁷ C/m

electric force at 2 cm away.

$E(r) = \dfrac{2K\lambda}{r}$

F = E q

$F= \dfrac{2K\lambda\ q}{L}\int \dfrac{dr}{r}$

integrating from 0.02 to 0.02 + L

$F= \dfrac{2K\lambda\ q}{L}[ln(0.02+L)-ln(0.002)]$

$F= \dfrac{2\times 9 \times 10^9\times 3.9\times 10^{-7}\times 19 \times 10^{-9}}{0.11}[ln(0.02+0.11)-ln(0.002)]$

F = 2.26 ×  10⁻³ N