Problem: The figure (Figure 1) shows a thin rod of length L with total charge Q. Find an expression for the electric field E at distance X from the end of the rod. Give your answer in component form. Express your answer in terms of the variables Q, L, X, unit vectors i, j, and appropriate constants.

FREE Expert Solution

We consider a small element of length dl with a charge dq since the charge is uniformly distributed on the rod.

The electric field at point P due to charge element, dq is:

$\boxed{\stackrel{\mathbf{\rightharpoonup }}{\mathbf{E}}\mathbf{=}\frac{\mathbf{d}\mathbf{q}}{\mathbf{4}\mathbf{\pi }{\mathbf{\epsilon }}_{\mathbf{0}}{\mathbf{r}}^{\mathbf{3}}}\stackrel{\mathbf{\rightharpoonup }}{\mathbf{r}}}$

The charge element, dq is expressed as:

$\boxed{\mathbf{d}\mathbf{q}\mathbf{=}\frac{\mathbf{Q}}{\mathbf{L}}\mathbf{d}\mathbf{l}}$