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:

$\boxed{\mathbf{q}\mathbf{=}\mathbf{\int }\mathbf{\lambda }\mathbf{x}\mathbf{d}\mathbf{x}}$

The electric field due to a point charge:

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

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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