Charge of uniform linear density 3.0 nC/m is distributed along the x axis from x = 0 to x = 3 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the point x = +4 m on the x axis?
A) $\int _ { 0 } ^ { 3 } \frac { 27 d x } { x }$.

B) $\int _ { 0 } ^ { 3 } \frac { 9 d x } { 4 - x }$

C) $\int _ { 0 } ^ { 3 } \frac { 27 d x } { 4 - x }$

D) $\int _ { 0 } ^ { 3 } \frac { 27 d x } { x }$

E) $\int _ { 0 } ^ { 3 } \frac { 27 d x } { 4 + x }$.

Question

Charge of uniform linear density 3.0 nC/m is distributed along the x axis from x = 0 to x = 3 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the point x = +4 m on the x axis?
A) $\int _ { 0 } ^ { 3 } \frac { 27 d x } { x }$.

B) $\int _ { 0 } ^ { 3 } \frac { 9 d x } { 4 - x }$

C) $\int _ { 0 } ^ { 3 } \frac { 27 d x } { 4 - x }$

D) $\int _ { 0 } ^ { 3 } \frac { 27 d x } { x }$

E) $\int _ { 0 } ^ { 3 } \frac { 27 d x } { 4 + x }$.

Quizplus · Accepted Answer

The electric potential due to a linear charge distribution is given by integrating the potential contribution from each infinitesimal charge element. The potential at a point due to a charge element is inversely proportional to the distance from the charge element to the point. Here, the distance from a point on the x-axis at position x to the point at x = 4 m is (4 - x). The linear charge density is 3 nC/m, so the potential contribution is proportional to $\frac{3 \times 9}{4 - x}$, simplifying to $\frac{27}{4 - x}$.

Charge of Uniform Linear Density 3 ∫0327dxx\int _ { 0 } ^ { 3 } \frac { 27 d x } { x }∫03​x27dx​

Charge of Uniform Linear Density 3 $\int _ { 0 } ^ { 3 } \frac { 27 d x } { x }$