A 16-nC charge is distributed uniformly along the x axis from x = 0 to x = 4 m.Which of the following integrals is correct for the magnitude (in N/C)of the electric field at x = +10 m on the x axis?
A) $\int _ { 0 } ^ { 4 } \frac { 36 d x } { ( 10 - x ) ^ { 2 } }$
B) $\int _ { 0 } ^ { 4 } \frac { 154 d x } { ( 10 - x ) ^ { 2 } }$
C) $\int _ { 0 } ^ { 4 } \frac { 36 d x } { x ^ { 2 } }$
D) $\int _ { 6 } ^ { 10 } \frac { 154 d x } { x ^ { 2 } }$
E)none of these

Question

Quizplus · Accepted Answer

The correct integral is $\int _ { 0 } ^ { 4 } \frac { 36 d x } { ( 10 - x ) ^ { 2 } }$ because it represents the electric field due to a line charge, where the charge density is $\frac{16 \text{ nC}}{4 \text{ m}} = 4 \text{ nC/m}$, and the factor 36 comes from converting nC to C and the constant $k = \frac{1}{4\pi\epsilon_0}$.

A 16-NC Charge Is Distributed Uniformly Along the X Axis ∫0436dx(10−x)2\int _ { 0 } ^ { 4 } \frac { 36 d x } { ( 10 - x ) ^ { 2 } }∫04​(10−x)236dx​

A 16-NC Charge Is Distributed Uniformly Along the X Axis $\int _ { 0 } ^ { 4 } \frac { 36 d x } { ( 10 - x ) ^ { 2 } }$