Electric Fields in Conductors Video Lessons

Concept

# Problem: A charged rod of length L = 5.60 m lies centered on the x axis as shown. The rod has a linear charge density which varies according to λ= ax where a = -58.3 µC/m2.A. What is the total charge on the rod?B. What is the x component of the electric field at a point on the x-axis a distance of D = 7.80 from the end of the rod?

###### FREE Expert Solution

In this problem, we'll consider the element of length, dx.

So, we get the total charge as:

$\overline{){\mathbf{q}}{\mathbf{=}}{\mathbf{\int }}{\mathbf{\lambda }}{\mathbf{x}}{\mathbf{d}}{\mathbf{x}}}$

The electric field due to a point charge:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{k}\mathbf{q}}{{\mathbf{r}}^{\mathbf{2}}}}$

A.

The linear charge density is given to be:

λ = ax, but a = -58.3 µC/m2 = -58.3 × 10-6 C/m2

Charge on the element of length, dx

dq = λdx = axdx

Total charge on the rod is:

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###### Problem Details

A charged rod of length L = 5.60 m lies centered on the x axis as shown. The rod has a linear charge density which varies according to λ= ax where a = -58.3 µC/m2.
A. What is the total charge on the rod?

B. What is the x component of the electric field at a point on the x-axis a distance of D = 7.80 from the end of the rod?